Campaign mode is a mode for Rising storm 2 that expand gameplay from one round to multiple rounds as a war. You don't pick team in the beginning of each round. You stay in the team you chose until you get autobalanced or switch team.
In the campaign mode you feel more connected to your team. You don't only want to win the round but win the entire war as well.

The essential thing of campaign is campaign map


As you can see this map is divided to regions. Each region have it points value (more about it later on). Each region have it's own map pool to choose.
There are Combat power and Victory points.
Combat power is amount of points that allows you to attack or defend. Attacking or defending have it's cost in combat power.
Victory points is the sum of all the region's points.
After each round amount equal to all your victory points is added to your Combat power account

Each side of the conflict starts with one 15 point region, Southern forces with Saigon, Northern with Pleiku. Each team starts with equal amount of combat power.
After each round winning team can decide what to do next

You win the war when:

• you have more VP at the end of 1975
  
• the enemy has 0 or below CP
  
• you capture all 12 regions

In order to win the war you need to capture some regions so you will gain more combat power each round to cover attacking expense.
When you are attacking region the amount of points it has matters. The ownership of region also matters.
5pt regions are cheapest to attack and 15pt regions are the most expensive to attack.
For example attacking neutral 5 pointer maximum cost of attack will be 50 CP. Attacking neutral 10 pointer may cost you up to 100 CP. On the campaign map screen game will tell you the cost to attack and defend region.

Your maximum cost of attack will be the amount game tells you multiplied by either 1x,2x,3x (accordingly 5pt, 10pt, 15pt). Maximum cost for attacking region from screen above will be:
The actual cost is calculated by multiplying max. cost by % of tickets used.
So let's say you attacked above region and lost 50% of tickets. In this situation you will lose:
Maximum costs:
As you can see attacking enemy 10 pt and neutral 15 pt have the same cost so it's better to attack neutral 15 pt than enemy 10 pt for the same cost you can have 5 more Victory points.
Winning or losing round doesn't affect the cost of attack.

Sometimes campaign isn't coming according to plan and you're short on CP. Then you're forced to defend because it's cheaper. Cost of defending is less complicated than attacking cost. Maximum cost is always either: 25 CP or 50 CP.
Final cost is calculated same way as attacking cost.
Unlike attacking cost, defending cost is affected by loss. If you fail to defend your cost will always be maximum cost no matter how many tickets you lost.

Each side have it's own special campaign ability. Attacking team can choose to activate ability. After using ability or after campaign start you have to wait 2 rounds to use it again (you can use it in 3rd round of campaign or in 3rd round after last used ability.

• Attacking cost is reduced by half
  
• Access to People Army of Vietnam faction
  
• Access to Ho Chi Minh Trail commander ability in early war (through PAVN, thanks Heifercakes for note)

• After failed attack region will become neutral instead being captured by enemy
  
• After succesful attack enemy Combat power cost will be tripled

Factions are the matter of preference. I will give you some tips that can be helpful.
There are 3 stages of wars: Early, Mid and Late war. Each has it own set of weapons.
In early war most of the factions don't have automatic weapons for Grunt/Guerilla. The only factions having them are US army and PAVN.
Many players vote USMC in early war and after that some players complain about not having M16s. USMC have some good kits (some even OP) in early war but overall most players will play grunt and most players prefer M16 over M14.
There's no combat pilots and no spooky for southern forces.
Ho Chi Minh Trail commander ability is disabled unless you activated HCMT campaign ability

For mid war all southern forces get M16s so it's down to team preference.
For northern forces PAVN gets AKMs variant for AK, RP-46 (ultimate ratatata), SVDs and K-50ms but have less powerful arty for commander and has less weapons to choose from compared to NLF.
Combat pilots for southern forces
You can use HCMT commander ability no matter if you used HCMT or not.

In late war the only faction for southern forces is ARVN. They get 30rd M16s (it's only way to use them in the game). They don't get Garands though :((
NLF have AKMs and SVDs. The only PAVN-exclusive weapons are RP-46 and K-50m