In this quick and simple guide I will try to present you, in my opinion, which are the 10 best steel and silver swords in the game based on Damage and DPS, and, i will also present you another sword for a sign build if you are interested in it (although not recommended)

I have a lot experience in the game and therefore i now what i'm talking about.

NOTE: There are a lot of sword in this list that require the Blood and Wine DLC

THE 10 BEST IN TERMS OF DAMAGE AND DPS:

1: Toussaint Knight's Steel Sword:

Without a doubt the best Steel Sword in the game. Insane +20% crit rate and 100% crit damage and also 15% to burn makes it so strong that basically no other steel sword can reach its DPS not even close.
The 30% Queen Sign and 300 Armor Piercing is algo very usefull

You can get the diagram from the chest of Antoine Straggen's at the Arthach Palace Ruins in Toussaint, which of course requires the Blood and Wine DLC















2: Hen Gaidth Steel Sword:

The second best Steel Sword in the game. 75% crit damage and 15% crit rate makes it ridiculously strong although not as strong as the Toussaint knight Steel Sword. But the best part of this weapon is the 15% chance to stun which causes and enemy to become, well, stunned and makes them unable to attack, giving you a few seconds to deal damage for free. However the stun does not work on most bosses so be carefull.

You can get this weapon in the Unseen Elder cave which requires the Blood and Wine DLC.

NOTE: DO NOT VENTURE TOO DEEP ONTO THE CAVE AFTER THE QUEST HERE (OR AFTER OPENING THE CAVE IF YOU CHANGED YOUR MIND AND WENT FOR SYANNA) BECAUSE THE UNSEEN ELDER WILL KILL YOU








3: Faithful Friend:
In my opinion the third best Steel Sword in the game. 95% crit damage and 12% crit rate is very strong and always useful. The +28% Aard Sign intensity can come in handy sometimes but just sometimes
The 15% poison and 5% exp from humans and none humans is meh and not worth in most situations

The diagram for this weapon can be looted after you save a Knight Errant in Distress southwest of Mont Crane Castle, it is in a chest next to a corpse and close to the knight.














4: Toussaint Steel Sword:

This sword is slightly different than the Toussaint Knight Steel Sword in appearance and it's stats are weaker and also it lacks the Queen sign intensity. It's still very strong tho and it deserves 4th place as it is far stronger than the swords below.

You can obtain the diagram during the quest "The Last Exploits of Selina's Gang" in Toussaint, which of course requires the DLC Blood and Wine.















5: Tesham Mutna Steel Sword:

The Fifth best in terms of DPS but number 6 is very close to it in terms of DPS.

It's 75% critical hit damage bonus and 15% crit rate are strong as well as the very strong 15% chance to stun, but keep in mind this sword is always at level 39 no matter what level you pick it up (unless you are on new game plus) unlike the Hen Gaith Sword or number 6 Sword, which makes this weapon a poor choice at higher levels.

You can get this sword and the rest of the armor set during "La Cage ou Fou" quest in Toussaint. Therefore it requires the Blood and Wine DLC











6: Teigr:

This weapon may lack any Critical hit damage bonus at all, but that doesn't make it weaker.
This sword will scale with the player until the player picks it up, so if you take this sword at level 50 it be around the same DPS as the Tesham mutna Sword, but at higher levels will be more powerful.
The 5% Exp from humans and none humans and the 10% Bleeding change are mediocre, though the 15% Aard can be slightly usefull.

It can be obtained during the Free DLC quest "Where the Cat and Wolf Play"... as either loot from Gaetan if killed, or during the following quest "Take What You Want" if you decided to spare him.









7: Grandmaster Usine Steel Sword:

+75% crit damage, +5% crit rate and +21% adrenaline Points makes the Grandmaster Usine Steel Sword a powerful choice for late game, however the 5% extra chance to crit is very little compared to the sword above and you won't be getting that sweet +75% crit damage that often.
It's still very strong tho and should be a serious option.
Keep in mind that the sword is always at level 40 so higher level sword are more powefull, including Teigr.

This diagram can be found during the quest "Scavenger Hunt: Grandmaster Ursine Gear" in Toussaint. It requires the Blood and Wine DLC













8: Hjalmar's Steel Sword:
Hjalmar's Sword is arguably the most random weapon you can get. It can either have +20% crit damage and make it one of the worst weapons or have the insane +200% crit damage and rival the most powerfull weapons in terms of DPS.
You can get this sword from Hjalmar himself if you defeat Vildkaarl in a fistfight at the banquet in the Kaer Trolde citadel during the "King's Gambit" quest. This fistfight MUST be done before you complete the first objective by collecting your reward from Crach.

I remind you that, just like Teigr, this weapon will scale to your level until you pick it up so take it at the highest level possible and keep reloading a save until you get the 200% crit damage or close to it.








9: Manticore Steel Sword:
This weapon is weaker than then Ursine Steel sword due to the Ursine +75% crit damage.
It's still powerfull and should be considered an option.
The 5% exp is useless and 10% chance to bleed does not affect some enemies and is worthless in most situations.
250 Armor piercing is fine
This weapons is always level at 40 (unless you are on NG+) so many late weapons are more powerful (Teigr again?) and deal more damage

The diagram for this sword can be found in the ruins of Bastoy Prison during the "Scavenger Hunt: Grandmaster Manticore Gear" quest.














10: Grandmaster Wolven Steel sword:
This sword lacks any crit damage but has +11% sign intensity and therefore is very usefull for a sign character build combined with the griffin armor.
The 11% adrenaline and 11% crit chance combined are always handy but the +11% bleeding chance and the exp are almost always useless.

The sword is always at level 40 just like all grandmaster gear so keep that in mind (unless you are playing on new game+)

You can get the diagram in the Termes Palace Ruins during the "Scavenger Hunt: Grandmaster Wolven Gear" quest in Toussaint, which requires the Blood and Wine DLC

Because this set is a Free DLC it does not require the previous items to be crafter in order to craft the superior gear so you can craft the grandmaster sword directly










THE BEST SWORD FOR A SIGN BUILD:
A Sign build is a hard one as signs in general are pretty weak but if you decide to go for a sign build i hereby present you the best choice for it.
Vitis has a +20% sign intensity for any and all signs and therefore is the most usefull for a sign build. It has 3 slots as well so you can improve your sign intensity even further with this sword.

You won't get high damage as the DPS build tho so keep that in mind

THE 10 BEST IN TERMS OF DAMAGE AND DPS:

1: Gesheft (CRAFTED):
+100% crit damage and +15% critchance makes Gesheft the best choice for a quick and easy fight.

Although Aerondight can deal higher damage at high charges you have to rely on Queen in order to charge the sword and to keep those charges, wasting stamina so Gesheft in my opinion is slighty better at the start of the combat and the vast majority of fights last a few hits at much (with Euphoria build) and you can't build all the charges with Aerondight in such short fights so Gesheft is slighty better at this.

The diagram is found in monster den cave north of Basane Farm in Toussaint therefore it requires the Blood and Wine DLC










2: Aerondight:
Aerondight is arguably the best sword in terms of damage. With this sword every hit onto an enemy will increase the sword damage by 10 % and at 10 charges every hit is a critical hit. If you kill an enemy with a fully charged sword the damage will increase permanently by 2 (10 max per level of player) . If you get hit by an enemy you lose 5 charges.

Pros: once you build 8+ charges the damage goes to insanity but as I said most fights won't last long to charge that much and you rely on those charges and as soon as you are hit you loose almost all of them, therefore you rely on Queen.

If you can use Queen constantly then Aerondight is better than Gesheft, but most combat builds don't rely on stamina or Queen so in this ones Gesheft is a better choice

I wanna point out that gesheft level is 45 and aerondight has a level cap of 47 (you can increase damage as i said). So on normal playthrough Aerondight is better than Gesheft at around level 50 or higher but on New Game plus if you start at level 55 both sword will be at lvl 100 by the endgame making Gesheft again the best choice

Aerondight can be ontained by finishing the quest "There Can Be Only One"
This quest can be started if you have completed quests which encompass all five of the chivalric virtues.




3: Cantata:
This Silver Sword is very strong however is not close to the big 2
It is of the very few silver Swords with Armor Piercing effect and with 75% critical hit damage and +15% critical hit change is insane.
All of this combined with a very powerful 15% chance to stun and a situational 15% bleeding chance makes it the third best Silver Sword.
The sword can be found in the Unseen Elder cave next to a mage's body during the "What Lies Unseen" quest. Requires the Blood and Wine DLC

NOTE: THE SWORD CAN ONLY OBTAINED ONCE. IF YOU DIDN'T OBTAINED IT THE FIRST TIME YOU ENTERED THE CAVE DURING THE QUEST DON'T GO DEEP INTO THE CAVE AGAIN AS THE UNSEEN ELDER THIS TIME WILL KILL YOU WITHOUT A CHANCE TO FIGHT.






4: Ami:
Another one of the very few silver swords with Armor Piercing effect, this one 300
With 75% crit chance, +15% crit rate and an awesome 15% chance to stagger it rivals Cantata in terms of damage, however this sword max level is lower than Cantata, making Cantata a better choice for late game, unless you went to find Syanna.
30% Queen sign is good for a sign build.

The Sword is looted from the corpse of the Monster of Tufo during the "Contract: The Tufo Monster" quest in Toussaint. Requires obviously the Blood and Wine DLC











5: Tah'rel:
+95% crit damage and +12% crit rate is very impressive and makes Tah'rel the 5th best silver sword in my opinion.
The 15% poison chance as well as de 5% experience is a waste and dissapointing as this sword could have been the third best if it had a stun chance. What a shame but it's still very strong and 100% recommended.

The diagram to craft this sword can be found during the "What Was This About Again?" quest in a cave near Plegmund's Bridge in Toussaint and of course it requires de Blood and Wine DLC













6: Casus Foederis:
Another one of the few Silver Swords with Armor Piercing this one with a +150 which helps with elementals.
With +50% crit damage and +15% crit rate as well as a level cap of 43 i placed it 6th in terms of damage. It is very powerfull but it is surpassed by the top 5 easily.

This sword can only be found while trying to enter Regis' temporary home at the "Mère-Lachaiselongue Cemetery" location. There the player can dispell an illusionary wall with The Eye of Nehaleni (requires to have completed Keira Metz quest). Behind it on top of a grave area this sword can be found.














7: Viper Venomous Silver Sword:
75% critical hit damage, 10% critical hit rate and 15% poison chance makes the Viper Venomous Sword a serious option at around level 39-44.
Despite the sword level capping at level 39 it can be usefull until much later in the game
The 25% Aard Intensity is rarely usefull and can be ignored most of the times

This sword is extremelly rare and, unlike all other witcher gear, does NOT have a diagram that can be received. The sword can only be obtained during the "Whatsoever a Man Soweth..." by challenging Master Mirror. Therefore this sword requires the Hearts of Stone DLC













8: Sarrim:
Just as the Viper Venomous Sword this sword has +75% crit damage, and +10% crit rate and has a few bonus to some signs such as +15% Aard, +15% Igni, and +15% Axii.
However this one lacks the poison chance and therefore deals less damage potential than The venomous Sword.
Visually they are almost identical.
The Diagram for Sarrim can be found in the Bandit camp near Kilkerinn Ruins. It requires de Hearts of Stone DLC















9: Grandmaster Ursine Silver Sword:
+75% critical hit damage bonus and +5% crit chance makes it a choice to consider at high levels, though +5% crit chance is very low and you requiere to spend points in crit chance and crit damage abilities to really see that +75% critical hit damage bonus.

This Sword Level is capped at 40 (not counting NG+)

This diagram can be found during the "Scavenger Hunt: Grandmaster Ursine Gear" quest in Toussaint, and therefore it requires de Blood and Wine DLC.
















10: Manticore Silver Sword:
+250 Armor Piercing and +50% crit damage combined with a +5% crit chance makes it slighty usefull, although not as much as the swords above.
The +10% bleeding chance is mostly useless and doesn't affect all anemies, and de 5% exp is really useless as most enemies won't even give 1 exp more.

This Sword Level is capped at 40 (not counting NG+)

The diagram can be found in Murky Delve during the "Scavenger Hunt: Grandmaster Manticore Gear" quest in Toussaint, and requires the Blood and Wine DLC

















THE BEST SWORD FOR A SIGN BUILD:
A Sign build is not recommended in The Witcher 3 as signs are very weak and in pretty much every situation not worth it, as swords deal much much more damage. If you choose to do so i present you an option.
Gesheft increases all signs by +20% so at least you get something usefull and you can increase it even further