Updated twice, even! (And have to attempt to post it twice as well... I guess I can't use smilies until I reach 15 posts then?)
Anyway, Update 2 (condensed):
Skipped over to Vermillion to pick up the Old Rod, Bike Voucher and HM01
Adwaita beat my Rival's Pidgeotto, then SuzumeBchi got his Ivysaur, Kadabra and Raticate, and learned Cut.
Back to Cerulean for the Bike and to beat the Gym. Adwaita bit Staryu twice, and SuzumeBchi needled Starmie (once!) and I got the Cascade Badge.
Took tunnels to get to Celadon City
Caught a Growlithe named Clifford
Bought a Fire Stone and got the Hot Tea for the guards
It took two runs to get through all the trainers in the Celadon City Gym, but SuzumeBchi once again solo'd all of Erika's pokemon.
Recieved the Rainbow Badge
Got the Coin Case and HM02 (for fun).
Headed to Saffron, but whited out in the Dojo.
Went back to the Game Corner to buy coins for a Dratini named Nessie.
All five of us went into the Rocket Hideout.
Team:
Adwaita - Level 35 Brave Female Wartortle
Moves: Rapid Spin, Water Gun, Bite, Protect
SuzumeBchi - Level 35 Timid Male Beedrill
Moves: Pursuit, Pin Missile, Twineedle, Cut
Clifford - Level 21 Bashful Female Growlithe
Moves: Bite, Roar, Ember, Odor Sleuth
Nessie - Level 18 Naughty Female Dratini
Moves: Wrap, Leer, Thunder Wave, Twister