Well for in-game playthroughs, most Pokémon will work just fine, with a few notable exceptions, and a lot of people just use their favorites.
Still if you are more concerned against getting through the game swiftly, then here is some advice.
Nidoking is pretty powerful all around and is offensively powerful, his only problem is that most of his really outstanding moves are either TMs you'll only get once (Earthquake) or are incredibly expensive like Flamethrower, Ice Beam, Thunderbolt. Though you can always go for the rather cheap Blizzard, Fire Blast and Thunder which are more powerful and less costly but suffer from low PP and a reduced accuracy.
Summary: Extremely powerful, but needs TMs to work.
Charmeleon It's final form is above average when it comes to playthroughs though not overpowered or broken by any stretch of the imagination. It learns some good moves without TMs and you can teach it Fly to make some use of its secondary type. Overall a solid choice.
Gyarados Becomes much more powerful, offensively, in Generation IV. Being a Water/Flying with high Attack and no flying moves is certainly not ideal, but with its ability and high stats it is still somewhat useable. It's a good candidate for random physical moves though his move pool in that regard is very shallow
Suggestion: Replace with another water type (unless you like his cool factor), some choices are:
Pikachu Pikachu is certainly usable and learns some decent moves, but even after evolving to Raichu it's not that special. It is certainly OK, but there are some better electric types available. Though most of them have their own issues.
Mankey It's very frail with a kind of weak movepool and does not have really enough offense to make up for it. Also, there isn't that much in the game that will be weak to fighting. IT doesn't really have much going for it. It's usable but certainly below average.
Abra If you can actually evolve it to Alakazam through a trade it becomes an offensive powerhouse. There isn't much in the game that resists it with the scarcity of Dark and Steel types in FR/LG. If you can't trade you'll be stuck with Kadabra who is still pretty powerful but not that much better than other Psychics in FRLG like Mr. Mime or Hypno.
Suggestions
Lapras Strong, bulky, good coverage with Water/Ice especially in the Elite 4. Very good Pokémon you get it pretty late in Saffron City. If you don't have some personal preference for Gyarados' 'awesome'-factor then definitely replace him.
Vaporeon Very very sturdy with decent offensive stats. Another valid water-type to consider if you wish to replace Gyarados.
Snorlax pretty powerful, good moves, good defensive stats. Can learn a wide array of coverage moves like Shadow Ball. Replacing either Mankey or Pikachu would be a good choice.
Machop - replace Mankey only if you can trade to evolve Machop to his final form and you actually want to have a fighting type on your team.
Hitmonlee another potent fighting type with strong attack. Available reasonably early once you get to Saffron city.
Jinx You can trade a Poliwhirl in Cerulean to get her. That also means that her experience gain will get boosted which is a nice bonus. If you take Lapras their typing is a little redundant, but it's not a big issue. Again replace either Mankey or Pikachu.
Zapdos only if you don't mind using legendaries. Very powerful and already caught at a high level.
Some others: Doduo, Geodude, Electabuzz, Jolteon, Mr. Mime, Exeggcute.
Obviously those suggestions are under the assumption that you have taken no particular liking to any members of your team, otherwise I'd advise against replacing them.