If you have no local scene, or rather you don’t have a local scene, then play King of Fighters 98 on GGPO or Supercade. King of Fighters 02 is decent in itself but there are generally less disciplined players playing 02 in a larger quantity, as those types are attracted by the character roster and don’t really give a damn about playing well.
So if you want to learn fundamentals, I suggest playing King of Fighters 98 against other players online. If you don’t, then just play King of Fighters 2002 UM or King of Fighters 98 UM.
I was in the same boat as you when I started learning KOF in 2009 to get ready for XII, but then XII sucked. I kept up playing 98 on GGPO since then and I’ve gotten way better because of it. So I feel certainly ready for XIII, and you could also get a head start too. If you see me available on GGPO or Supercade, feel free to challenge me. I’m also on #SNKPlaymore @ Efnet on IRC so PM me there if you want to get games.
2002UM would be preferred but you can’t really get any games with it online, but if you have a local scene then that would be the best option. 98/02 on GGPO are good options; that’s how I learned at least. Watch the Dandy J guides if you haven’t already (they are stickied in this sub forum).