Just finished a run. Did Snorlax already in a previous post, so I'll just rank the rest of the team.
Availability: Only one Eevee in the game, received in Celadon Condominiums (the apartment buildings) at Level 25. Early/mid-game, before the fourth badge.
Stats: Base 130 Speed and 110 SpAtk are nothing to laugh at, especially with STAB Thunderbolt/Thunder. SpDef is decent at 95, while Base 65 HP and Atk are pretty horrible.
Movepool: Pretty horrible outside of ThunderBolt, Shock Wave, and Thunderbolt. The only Special coverage move it gets is Hidden Power, while the only decent other options it gets are Double Kick, Pin Missile, and Shadow Ball. Both Thunderbolt and Shadow Ball are GC TMs, so getting the coins kind of sucks.
Major Matchups: Earliest Gym you can get Eevee/Jolteon for is Erika.
Erika: Don't use Jolteon here, as everything resists Shock Wave.
Sabrina: Pin Missile/Shadow Ball can hurt, but still gets maimed if it doesn't OHKO stuff, particularly Venomoth if you don't have TBolt.
Koga: The Koffings and Weezing both have low SpDef, so Thunderbolt hurts a lot. The Muk has better SpDef, though, so it might actually kill you.
Blaine: Thunderbolt is still powerful, but this is really when Jolteon starts to decline. Better off leaving this to something like a Rhydon or Blastoise.
Giovanni: PLEASE do NOT use Jolteon in this gym except on the Fighting types the Gym Trainers have.
Lorelei: Cloyster is easily OHKOd by a Thunderbolt, Thunder should OHKO Lapras and everything else except for Jynx. Leave that to a Fire Type.
Bruno. Do NOT use Jolteon here. Everything destroys you.
Agatha: Golbat is easily OHKOd by Thunderbolt, while Haunter and Arbok should be an easy time if they decide to spam status moves.
Lance: Gyarados has no shot, and Aerodactyl might get killed if Jolteon manages to live an Ancientpower.
Blue: Pidgeot is Thunder bait, while Gyarados if you didn't pick Squirtle/Blastoise if you picked Charmander are in the same boat. Rhydon destroys you, while Alakazam might live a Thunder and kill you with Psychic.
General Stuff: Good when you first get it, but falls of later on due to poor coverage. Still helps in the E4 and Champion, but definitely better Pokemon out there.
Availability: A starter, so Bulbasaur is the first Pokemon you get.
Stats: Pretty balanced stats all around, so has decent bulk and can go mixed. Other than that, nothing spectacular.
Movepool: Sleep Powder and Leech Seed are a good combination. Gets Giga Drain as a TM from Erika's gym, as well as Earthquake from Giovanni and Razor Leaf through level-up. Unfortunately, the Body Slam TM does not exist like in Gen 1, so you'll probably stuck with Mono-Grass+Cut for most of the game unless you use the 1 EQ TM.
Brock: Vine Whip destroys him.
Misty: You should have Razor Leaf by this time, so you'll have no problem.
Lt. Surge: You resist Electric STAB, although Diglett/Dugtrio is far superior for this match.
Erika: They resist Razor Leaf, and Cut is shit, so no.
Sabrina: lolNO. SERIOUSLY NO.
Koga: Cut is shit, so no.
Blaine. See Sabrina.
Giovanni: Takes care of the Rhyhorns and Dugtrio. A Water or Ice Type is a better choice for the Nidos though.
Lorelei: Cloyster is probably the only one you wanna go up against due to its low SpDef.
Bruno: Kills the Onixes, although stay away from the Hitmons and Machamp.
Blue: Rhydon is destroyed by Giga Drain/Razor Leaf. Other than that, probably no kills for Venusaur.
General Stuff: No auto-critting Razor Leaf or Body Slam TM like in Gen 1 hurts it a lot, as Team Rocket loves to use Poison Types.
Availability: Magikarp can be bought from the bald guy in the Pokemon Center near Mt. Moon for 500 dollars. So early.
Stats: Good Atk, although no good moves to abuse outside of EQ. Has good Special Attack to utilize STAB water moves as well as Blizzard.
Movepool: As a Magikarp, Splash, Flail, and Tackle. Gets Bite as soon as you evolve it at Level 20 and Dragon Rage five levels later. Can also utilize the Water Pulse TM that Misty gives you. Eventually upgrades to Surf, Hydro Pump, and Blizzard. Can also utilize the EQ TM.
Lt. Surge: NO
Erika: You don't have the Blizzard TM yet, and you really shouldn't waste your time getting the coins for the Ice Beam TM.
Sabrina: You could get a kill on the Venomoth, although leave everything else to something such as Snorlax with Shadow Ball.
Koga: Surf might net you a kill against the Koffings, although you should use a Psychic type really.
Blaine: Surf Spam=Win
Giovanni: See Blaine.
Lorelei: Really nothing here.
Bruno: Onixes are a joke, leave everything else.
Agatha: Haunter and Golbat are easy prey for Hydro Pump.
Lance: Aerodactyl is easy prey for Surf, Dragonairs and DNite are hurt by Blizzard.
Blue: Rhydon is destroyed by Surf, Charizard hurt by Hydro Pump if you picked Bulbasaur.
General Stuff: Training Magikarp is a bitch, although you can always dump it in the day-care. Once you get a Gyarados, however, stuff becomes a LOT better.
Availability: Route 3 is where you can get a Nidoran-M, so before Misty.
Stats: Average stats at best, but powerful moves and wide TM compatibility to compensate.
Movepool: As a Nidoran-M, best you can do is Double Kick, but upgrades to Horn Attack. Goes through a rough period if you decide not to evolve Nidorino straight away. However, when you evolve to Nidoking it has STAB Earthquake, as well as stuff like Fire Blast and Thunder TMs, as well as Megahorn at Level 43.
Lt. Surge: If you've evolved to Nidoking by this time, you have a decent shot at winning with some Horn Attacks.
Erika: Victreebel and Vileplume get hit somewhat by Peck, while Tangela could in theory be worn down by Poison Stings.
Sabrina: Might kill the Venomoth, but nothing else.
Koga: Nidoking doesn't have EQ yet, so no.
Blaine: Still no EQ, but may kill the Growlithe and Ponyta.
Bruno: Can kill the Onixes, though the Hitmons and Machamp are better left to something else.
Agatha: Kills the Golbat with Thunder, as well as the Arbok with EQ.
Lance: If you gave it Ice Beam, it could do decently well, and destroys the Gyarados with Thunder.
Blue: Kills Exeggutor with Megahorn. Gyarados destroyed by Thunder. Nothing else really.
General Comments: Starts to get good once you get a lot of TMs.
Availability: Route 3 is the earliest you can get Mankey.
Stats: Good Speed and Attack, pretty bad everything else.
Movepool: All you really need is Brick Break/Dig/Rock Tomb or Slide/Cross Chop.
Misty: No real use here.
Lt. Surge: If you have given Mankey Dig it can do some work here.
Erika: Brick Break hurts Tangela, although Victreebel and Vileplume are better left to a Fire-Type.
Koga: Sucks here.
Blaine: Rock Slide hurts everything, but burn chance is a little risky against Arcanine and Rapidash.
Giovanni: Takes care of the Rhyhorns and Duggy, but Nidos better left to a Psychic type.
Lorelei: Destroys everything except Slowbro and Jynx with Cross Chop. Jynx hurt hard by Rock Slide.
Bruno: Destroys the Onixes.
Agatha: Can hurt the Golbat with Rock Slide and the Arbok with Dig.
Blue: Can hurt the Rhydon with Cross Chop, but that's really it.