Crafting becomes available early on in the story. To fuse items together, visit your sister in the MOGRA bar.
The first item you select is the recipient and it will get its stats boosted. All other items will be consumed in the process. There's no limit to how many items you can fuse together at once. The look or moveset of the resulting item will not change, only the damage output or defense will be raised. That means you can pick any weapon or article of clothing that you like and then boost it to the desired power level.

The limit to an item's stat is 999. For every 100 levels in power, the item's name will get a new prefix.
100: +1
200: Freaky
300: Legit
400: Pro-Tier
500: Deluxe
600: Super DX
700: Legendary
800: Wicked
900: Godlike

Weapons are divided into four categories: Fists, One-handed, Two-handed, and Heavy.
Clothing is divided into three categories: Headgear, Top and Bottom.
Underwear and shoes don't grant stat bonuses and can't be crafted.
Items within a single category yield better results when crafted together. This is the main method we will use. Keep in mind that it only has to be the same category, not the same item type. For example, you can use Combat Gloves to upgrade Water Pistols, because they both fall under Fists. From now on, this guide will always assume that all crafted items belong to the same category.

The fusing process costs ¥1000 for each "donor" item added to the mix. The "recipient" item will get a stat bonus that equals the "donor" item's power divided by 2.5 and rounded down. With that in mind, we can find the best items to buy for every category that will give us the largest stat boost for the smallest cost. The formula is as follows:

UPGRADE COST PER POINT = (ITEM'S SHOP PRICE + 1000) / (ITEM'S STATS / 2.5)

For each category, the item with the smallest cost-per-upgrade-point ratio will be the one that's most advantageous to use as upgrade materials.

This guide will only cover items that can be bought from shops. Items that are dropped by enemies have random stats and it's up to you whether to use them for crafting or not. Keep in mind that you have pay ¥1000 for every item added to the fusion, even if it only adds one point to the stats. It's up to you which items to keep, which to sell and which to fuse.

Directions for finding the shops imply that you have arrived in the area via fast travel, since each area has multiple entrances. All areas and shops are unlocked almost from the beginning of the game. The same item can be on sale in multiple shops, but always for the same price and with the same stats. I will only list one shop per item, the one that I find to be the easiest to reach.

The best upgrade material for Fist-type weapons is Combat Gloves.
Price: ¥5700
Attack: 50
Upgrade cost ratio: ¥335
Where to buy: TOKIWAMUSEN
Radio Kaikan Area, first shop to the right.

For One-handed weapons, your best bet is the Microphone.
Price: ¥8600
Attack: 75
Upgrade cost ratio: ¥320
Where to buy: YAMATA DENKI
Radio Kaikan Area, second shop to the right.

There are only two types of Two-handed weapons that can be bought from shops, and from them the Giant Poster is the one you need.
Price: ¥3700
Attack: 30
Upgrade cost ratio: ¥392
Where to buy: Mulan AKIBA Chuo-dori
Main Street SW, second shop to the left.
A lot of shops carry it, actually, but this one is the fastest to get to.

The best material for Heavy weapons is Monthly Dengeki Maoh.
Price: ¥6300
Attack: 55
Upgrade cost ratio: ¥331
Where to buy: Toranoana Akihabara Store A
Main Street NE, halfway through the street, the first shop in a group of three. It has a big Striprism poster on it.
Red Chiyodan and the Tray are holding a close second place, with a ratio of only ¥333 each.

The best headgear for fusing is the Red Sun Visor.
Price: ¥4000
Durability: 35
Upgrade cost ratio: ¥357
Where to buy: animate Hon-kan
Main Street NE, halfway through the street, the middle shop in a group of three.

For Top clothing, we'll use the Black Bird T-shirt.
Price: ¥3700
Durability: 35
Upgrade cost ratio: ¥357
Where to buy: LAMTARRA EPIXIS AKIBA
Main Street NE, halfway through the street, the last shop in a group of three.

This one is a little less straightforward. Get to Electric Town Plaza and go to the far left. You'll find a store called 5Day's. It's a shop that sells unique, character-specific, DLC and tie-in equipment, as well as the place where you can buy back your own clothes after they get ripped in a fight. Basically, every bottom piece that has a durability of 40 and cost of ¥5000 will fit you. Pick any you like. The upgrade cost ratio is ¥375.

Can I wear female clothing?
You'll be able to crossdress after completing the "Look But Don't Touch" sidequest.

Can I change the equipment of my partners?
You'll be able to do this after a point in the main story. If your partners are getting defeated too quickly because of their lousy gear, you can order them to enter a defensive stance by pressing Right on the D-Pad.

Can I craft male and female clothing together?
Yes, male, female and unisex clothes can all be fused with each other in any order.

How much does it cost to boost a piece of equipment from 1 to 999?
Around ¥370 000 using optimum materials, depending on the category.

Help! My 999 Dirty Parka has been ripped!
You can buy it back in 5Day's in Electric Town Plaza.

How does the minigame of talking to your sister work?
It's mostly randomized. You can unlock three bath towels to wear and the ability to change your sister's clothes. For more info, I recommend checking this guide.

If you have any questions, don't hesitate to ask. Happy stripping!

If you found this guide useful, consider buying me a can of coke on donatty[donatty.com]
or boosty[boosty.to]

Cheers!