So, my friends and I have been interested in possibly picking up a 3 to 4 player co-op game such as Borderlands 2. However, I have no idea where to get us started or what we need to be successful. I've looked through the resources but can only find a 2 player tutorial. Does much change with the addition of more players?

Do we need certain save files / a certain patch / certain team composition? any answers would be appreciated.

The team composition for four player used to be Gaige/Axton/Zer0/Maya, but the reasoning for that is sorta not valid anymore with the addition of some new glitches. Now you'll probably want Gaige/Axton/Axton/Maya to be the fastest. For save files the ones in the resources section will work with some small changes. You'll want at least one character to have a perfect muckamuck (Same as the Gaige sniper just Jakobs barrel), and at least one character to have the sniper from the Axton co-op save for crit stacking. Routing will be mostly up to you and your friends to figure out as a team, as there are many options for which character does what stuff without losing time. Although you will want to watch the current record and maybe the 2p record as well for a good idea of stuff to do to be fast.

For 3p, Gaige/Axton/Axton is the fastest. For 4p, Gaige/Gaige/Axton/Axton is probably close to fastest, the comp could also be Gaige/Axton/Axton/Axton for maximum memes. I doubt Maya in there would help much for any% - she does provide res glitch, but that wastes a TON of stacks if you get first try RNG, because you have to kick at least one person from the game. The 2p record has a few slightly new advanced strats that 3p and 4p don't do, but that's because we did those runs before stuff was discovered. The route is basically the same for all three runs - there's really only a couple places that you split up. 2p will most likely always be the fastest any% category, just because 3p and 4p add enough extra health and spawns to make a small bit of time difference.