Would anyone have any advice for me on possible changes to my team and a basic game plan or something.
Thanks alot 
Welcome to the site massi4h.
Wouldn't worry about wanting Athena on your team all the time; she fits your style, and that's important.
I'd honest say no matter what character you pick, if you're still working on all the peculiar parts of KOF like guard cancel rolls/back attack, CD attacks, (hyper)hops, etc, that should be your focus. Make sure in planning for your tournament (EVO?) you practice that everytime.
Honestly though everyone picks him, for zoning and poking, EX (Flame) Iori is a great character (basically the Ken of KOF with his shoto-esque style). Billy is a decent zoner/poker with a lot of hopping with C or forward A. He still rushes down a lot, usually with cr.B(x2), dp.B, qcb.A or hcf. C. You might try out Takuma too; he lacks the dp that Karate has, but better fireball throwing options to me, and can still intimidate almost as well as Karate with his kicks.
Kula and Yuri are still very good zoners to me, but they require even more rushdown to be really effective.
Best game plan I can give you is while you have shotos, don't always play shoto style. With every character you've got, pick up at least some basic combos like the easier ones from their trials (usually 1 and 2) or at their character wiki's
KOF XIII general wiki -
http://dreamcancel.com/wiki/index.php?title=The_King_of_Fighters_XIIIFor Athena -
http://dreamcancel.com/wiki/index.php?title=Athena_Asamiya_(XIII)Billy -
http://dreamcancel.com/wiki/index.php?title=Billy_Kane_(XIII)Mr. Karate -
http://dreamcancel.com/wiki/index.php?title=Mr._Karate_(XIII)And DO NOT be afraid to be agressive. It's the nature of the game. Apply pressure where you can, preferably with weak attacks to lead into combos.
I know someone will offer better specific advice than this, but hope some of this will help you.