Borderlands – start a new game in Borderlands 2 but use an old character

On the main menu, you will have a Select Character option. That lets you switch the active single player save. Once chosen, select Continue.

If you join another host's game, you can also choose which of these saves (characters) to play as in the first screen it shows you after you connect to the server, via the Select Character menu option.

Any progress in single or multiple is saved automatically per save. If you played co-op on the first save and progressed through the missions with others in co-op on their save (mission progression), any you complete with them will be saved on your character and you can't "go back" without creating a new character.

See How does mission progress work in multiplayer? for a description of how MP progress works when playing on other's hosts.

Borderlands 2, like its predecessor, does not use dedicated servers, but relies on the host player (the one whose game the other 3 join) to act as the server. Therefore, you will probably be better off joining other peoples' games together.

Whether you'll be able to comfortably play with a friend depends on your network and geography/Internet topology: somebody from Eurasia will have an acceptable connection to somebody in the Americas (~100-200 ms ping), while somebody in Australia will have an abysmal ping to somebody in Eurasia (~350-450 ms), due to the packets having to go through NA.