(Tenative) Rivallocke Rules
1. Only Pokemon used by the Rival may be used.
2. First USEABLE Pokemon may be caught; in concession to the limited catch pool, the usual Monolocke rule of "three attempts allowed" is in play.
3. Any Pokemon that faints is unusable for the duration of the run.
4. OPTIONAL: the ROM must be hacked to give you the same starter as the Rival. If playing on a cartridge, just ignore this rule.
For RBG, this means you are limited to the Rattata, Pidgey, Abra, Magikarp, Exeggcute, Growlithe, Rhyhorn, and [Starter] evolutionary lines.
Places to catch:
Rattata: anywhere
Pidgey: anywhere
Abra: above Cerulean, Celadon Game Corner
Exeggcute: Safari Zone
Magikarp: Salesman, anywhere (via Old Rod)
Growlithe: East of Celadon, West of Lavender
Rhyhorn: Safari Zone
Commentary: in some sense, you are getting the best Pokemon lines in the game. In another sense, you're highly limited (especially early on) and may suffer difficulties.
( Basically, do this if you want a challenge but not too much of one. )