Here's a team that I'd advise:
Blastoise: Water Starter that handles Rock, Ground and Fire. More depending on what moves it knows(like Ice Beam and/or Earthquake). Ice Beam handles Dragons and Grass Types while Earthquake covers its weakness against Electric Types(although its slow speed might be a detriment to using such a move against fast Electric Types).
Alakazam: Psychic Sweeper that handles Fighting and Poison quite easily. Keep in mind that since this is FireRed and not Red that Agatha's Ghost Pokemon can hurt you pretty badly.
Arcanine: Fire Type that is better with Physical moves than it is with Special. However, with 555 base stats, its a quasi-legendary that handles Grass(when not paired with Water or Dragon), Ice(when not paired with Water or Rock), Bug(when not paired with Water or Rock) and Steel(so long as its not paired with Rock). Unfortunately there aren't any Physical Fire moves Arcanine can learn but regardless, it's strong enough to crush opponents.
Jolteon: Electric Type that easily counters Water, Flying, Dark and Psychic Types thanks to Pin Missile. It won't benefit from Generation 1 mechanics but don't let that discourage you as Jolteon is still a strong Electric Type when put in ideal situations.
Snorlax: Quasi-legendary Normal Type who's monster 160 Base HP makes people ignore its slow speed. The fact it learns Rest, gains STAB from Strength, Hyper Beam and other Normal Type moves, and can learn Shadow Ball and/or Brick Break to make it a versatile Physical Powerhouse. Keep in mind it would destroy Agatha's Ghosts due to being immune to them but would require being taught Shadow Ball to do so.
Right now, your team covers Fire, Water, Grass, Ice, Fighting, Poison, Rock, Ground, Flying, Bug, Dark, Psychic, Ghost, Dragon(if Blastoise knows Ice Beam), and Steel. Only typings you don't have a cover against are Electric and Normal. Normal doesn't have Gym's so the only Pokemon you have no counter against are Electric Types. Fortunately, Lt.Surge is early on in the game so if you're past that point, odds are you won't face any more Electric Types save for Scientists in Silph or Cinnabar Mansion(who typically use Magnemites that are part Steel). Your rival doesn't have an Electric Type so frankly, you can use whatever Pokemon you want at this point. I should mention that for your final slot you could use Gengar as he's completely immune to Ground moves thanks to Levitate and immune to Fighting Types so is a good pick to sweep Bruno. Another good option is Kingdra, an often overlooked Water/Dragon Type. By being part Water, it reduces its exposure to Ice moves, making Dragon as its only weakness!
If you pick Gengar(or w/e Pokemon you want), here's who'd I'd use against each Elite Four member:
Lorelei: Jolteon can sweep with Thunderbolt and Pin Missile. Thunderbolt crushes everyone but Jynx thanks to their Water Typing and Jynx is part Psychic so Pin Missile destroys it. In rematches though, Piloswine is immune to Electric so Fighting is advised here.
Bruno: If you go Gengar, he can sweep the entire team solo but so can Alakazam or a combination of Alakazam and Blastoise. Blastoise handles the Onix while Alakazam removes the Fighting Type Pokemon. In rematches, Onix evolve into Steelix so Gengar still rules the day here.
Agatha: Snorlax with Immunity ability and Shadow Ball does wonders. Immune to Ghost Pokemon, Toxic and can crush the Golbat and Arbok with STAB Normal moves. Earthquake only works against Arbok so keep that in mind. Alternatively, Alakazam can sweep the entire team since they're all Poison Types. Just be aware that Ghost vs. Psychic counts this time around. In rematches, she adds a Misdreavus and evolves Golbat into Crobat. Snorlax still kicks major arse nonetheless.
Lance: Open with Jolteon or Gengar to remove his Gyrados. Jolteon has x4 with Electric moves while Gengar is immune to Hyper Beam and can put him to sleep so another Pokemon can switch in. Overall though Blastoise is your counter if it knows Ice Beam and use it for every Pokemon in his arsenal after Gyrados. In rematches he adds a Kingdra and the only counter to that is another Dragon! Alternatively, if you have a Steel Type that resists Dragon moves, it should be utilized here.
Blue: Open with Jolteon as he's Super Effective against both Pidgeot and Alakazam. Then swap to Blastoise for Rhydon before going back to Jolteon for Gyrados. Then back to Blastoise for Arcanine and finish Venusaur off with Arcanine. In rematches he swaps his Pidgeot and Rhydon out for Heracross and Tyranitar(Rock/Dark). Both have x4 weakness to Flying and Fighting respectively so note that when creating your team.
