My best characters are, pretty much in order: Dr. Mario, Ice Climbers, and Peach nearly tied for first, with Zelda, Mewtwo, and Young Link nearly tied for fourth. From there, I tend to choose fairly randomly, which is no big deal since I'm good enough with almost every character that I can beat most of my friends with little to no problem. I will say, however, that Samus, Ganondorf, and Jigglypuff are all working themselves up nicely.
Most of my best characters have some sort of projectile that I can use easily either as a stalling tactic or to set up combos (Dr. Mario's Megavitamins, Ice Climbers' Icicles, Peach's Turnips, and Young Link's Bombs and Fire Arrows, although the Boomerang can work too). From there, my strategies are mostly improvised, although there are some constants: dash attack to aerial attacks with Dr. Mario, followed by a forward air when the opponent is damaged sufficiently; aerial combos with Peach; a defensive tactic with Ice Climbers, staying largely put, occasinally using a dash attack or forward B to enter the fray; a mostly hit and run strategy with Mewtwo while keeping a charged Shadow Ball to help round off a combo or edgeguard; and constant forward and back aerials from Zelda.
As far as advanced techniques go, I hardly use any other than L-cancelling. I've honestly felt no need to master them since I can beat pretty much all of my (very casual) friends without them, I still have lots of fun without them (well, when I'm with friends, anyways), and quite frankly, there are many things I'd rather do than spend hours at a time air-dodging into the ground and practicing whatever other techniques there are.