I have a few different favorite fighters, for different reasons.
Best Playing: SF3 3rd Strike, w/o fail. It may not be the most balanced SF, but it's the pinnacle of the series so far as combat fluidity is concerned. Parries really opened up the level of options at your disposal (I prefer 2nd Impact's air parry system, though), and the amount of unique character-specific combos and juggles made it feel more like a real fight.
Also ironically, it's easier to jump into 3rd Strike than any of the IV games, though at the highest levels 3rd Strike shames them. Not to mention, I actually like what the series did for the story (moving it forward), and most of the characters save Sean (dumbed way down) and Twelve were good additions to the canon, either in design/story, play-style, or both. I also enjoyed the soundtrack, some tracks much more than others, tho honestly 2nd Impact has the better soundtrack of the two overall (the two best songs of the series belong to 3rd Strike tho).
In fact, 2nd Impact has the better backgrounds as well, but since this is my Best Playing pick it easily goes to 3rd Strike.
Best Atmosphere: Real Bout Fatal Fury 2. Everyone thinks KOF when they think of SNK fighters, but the game that got me into their stuff and to respect their contributions to the genre was this game right here. SNK nailed the stages down perfectly; extremely varied and bursting with life. The character designs all felt refined and fit perfectly into the FF mythos. Music was very appropriate, and I enjoyed quite a few of the tracks personally.
But what impressed me most was how SNK managed to finally fine-tune the game mechanics. This was probably the last of the "traditional" Fatal Fury games, and as such still has the plane-switching and somewhat more "constricted" feel to it vs. the later SFII and Alpha games. Even so, the creativity on display regarding the moves was insane. Hon-Fu perfectly channeling that 90s action movie Jackie Chan vibe; Billy Kane's moveset perfectly encapsulating the asshole that he is. Rick coming out as a surprisingly good Dudley sort of character. Everyone just feels so well fleshed-out and a joy to play as. Not to mention the power hits look like they hurt DEVASTATINGLY HARD!.
Garou is usually everyone's top pick for FF game; I greatly enjoy its mechanics and the characters were great additions, but bit-for-bit RBFF2 beats it in almost every way for me.
Best Odd-Pick Fighter: Breakers Revenge/Cyberbots : These two fighters are the sort I wouldn't of gotten into unless some heavy convincing were done, or I tried them on a bored day. They've found a place in my heart, tho.
Breakers Revenge in a lot of ways is a pretty big ripoff of the SFA and FF series, insofar as how the game mechanics go. And in terms of character designs it shamelessly pillages from SFII. But it's a real blast to play, and the characters have a nice moveset. Breaking is also a really cool gameplay mechanic, and something I wish was followed up on more.
Cyberbots has to be the most slept on fighter Capcom's ever made. It's sort of spiritual successor to Mecha Warriors, and a spiritual predecessor to Tech Romancer. The fighting is very frantic for giant robots, and the animated character portraits are a treat. Music is fantastic and the difficulty is more than adequate. All in all, feels really bad-ass to be a giant robot but move with the fluidity of a ballet dancer.
Honorable Mention(s): Guilty Gear XX (eclectic soundtrack, great character designs, insanely fun gameplay), Street Fighter EX and EX2 (best new character designs of the SF series since the SFII games, very strong soundtrack, not too shabby play system), Melee (why not), and Tekken 5 (last Tekken I played seriously).
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There are still a good few fighters I want to play, mainly VF5, Daraku Tensei, Astra Superstars, and Martial Masters; maybe they'll become new favorites in a way or two. But as-is, these are my definitive picks.