So, update now I'm past Vermillion:
DESTROYED Misty with Kadabra. Seriously, ruined her team. Caught another Abra, went through Diglett Cave to then go trade that for the Mr. Mime you can get. Went and picked up Drowzee as well, then blitzed through the SS Anne. Had to pick up a Bellsprout to teach it Cut but that's all it's there for. Drowzee evolved in to Hypno in the Gym, then Mime and Kadabra tore through Surge. Raichu took two hits with a Psybeam from Kadabra.
I may have had an easy time because, you know, Gen I Psychic types > all.
So, the team as it stands: Kadabra (Lv. 28) - The star of the team, obviously. It'll get all the important Psychic moves when I get the TMs. Mr. Mime (Lv. 26) - Odd tank. Has a fair bit of Speed which means he can set up Barrier quickly and take some early hits, before wearing anything down that takes longer than a few hits. Hypno (Lv. 26) - Oddly, the Physical powerhouse, since his Attack is miles better than either of the other two. Headbutt and Hypnosis are a great duo.
The plan is to wait until I can get Exeggcute in the Safari Zone, then go nab Jynx (who'll probably lead out against Giovanni and Lance and that'll be all she's worth ) and Staryu (Starmie shall be my other TM whore <3) in the Seafoam islands