You get a set amount of credits for completing each objective wave, plus a small added bonus that varies according to the time you needed to finish the objective.
So the fastest way to earn credits is to finsh each game as fast as you can. The people above me already mentioned the speed runs that can be done on Glacier/Jade. Aside from that, what I can add is that the higher the difficulty, the better your survivability and damage output must be. From Gold up, the most important thing is dishing out huge amounts of damage as fast as possible. On Plat - it's staying alive to dish out said damage.
Characters that are very basic, very powerful and require little equipment are the vanilla humans, especially Adept, Infiltrator and Soldier.
For the Adept(6/6/6/0/6) all the weapons you need are any SMG<Hornet<Hurricane (with recoil dampener lvl 5 for the last one). If you have it, you can also add the Crutchcolyte in order to easily strip phantoms' barrier and trap them in singularity.
For the Infiltrator, you can make a sniper(6/6/0/6/6) or a shotgun infiltrator(4/6/6/6/4). For the Sniper, you need Mantis<Widow<Black Widow, for the Shottie - any Shotgun until you get the Claymore. then you are set.
For the Soldier(6/0/6/6/6) - Claymore + Grenade gear (the higher the level the better - more grenades).
Nuking spawns on waves 5, 8 and 9 generally make things go a lot faster. On Geth/Plat you may also want to nuke wave 2.
The easiest enemy on Gold IMO are Reapers, so long as you are mindful of the Banshees. On Plat, I'd prefer Collectors, unless you are good at dealing with phantoms and dragoon rushes - then Cerb. Geth are a pain and Reapers have an uncomfortable amount of Geth Hunters, which is a problem if you are not using the Geth Scanner.
Giant is the easiest map, Glacier and Jade are the fastest if you know what you're doing. FB White is also very good, but you need to funnel the enemy through the basment and the stairs, otherwise it gets complicated. Please don't be the idiot who hangs out in the basement and denies the best possible spawn point. Maps to avoid are Condor, London and tha Hazard variations.
Gear - once you've sorted out your commons and uncommons, you'll want to start buying Arsenal/Spectre packs. IMO, its best to save up money, buy packs in bulk (no less than 10 or 15 in a buying "session"). That way you're less dpendent on the RNG fortunes. Oh, and don't be a scrooge and buy Jumbo packs whenever you don't have enough consumables. Using consumables makes things go faster, plus it's impolite to let your teammates carry you.