CFOP: Make a cross, 4 pairs, orient and permute LL. It's a nice and simple method, and very tps-spammable. It doesn't require a lot of cube knowledge yet it can get you very far if you drill algs and tps. Plus, all top cubers use it anyway.
Roux: Make two blocks, solve the corners and do the rest intuitively. It's an efficient method, it's mostly rotationless and it has a very low alg count (most "standard" CMLLs are very nice algs). Definitely a very cool and elegant method, and it's starting to replace CFOP in one-handed solving. IMO this is the best of the big three in terms of speed.
ZZ: Make a magic edge line that makes the rest of the solve nicer, build two blocks w/ rotationless RUL gen and solve the last layer in one look with fewer algs (theoretically). It's the coolest looking layer by layer method IMO, but cube hardware doesn't suck anymore so "real" ZZ is dead. Now people complain it has bad lookahead and regrips
Pick whichever one suits you best. I use ZZ but I don't feel that comfortable recommending it to other people.