If you do a starter solo, this is probably the ranking for each generation:
R/B:
1. Squirtle. It doesn't have any trouble with the first two Gyms, you can skip the third Gym till later in the game, you have Ice Beam by the fourth Gym and it is either neutral against the other Gyms or it has the advantage. Either way, it is overleveled enough to not have any trouble. In the E4 with a set of Surf/Ice Beam/Earthquake/filler you have type advantage against every Pokémon except for Lorelei's Pokémon and Bruno's Fighting Pokémon, non of who can do anything back. The rival is should also be easy to beat, especially with Ice Beam to KO Venasaur. I don't think the other rival battles are difficult either with Squirtle's bulk.
2. Charmander. It will have trouble during the first two Gyms, but after that it is smooth sailing. Fire, Normal and Ground provide pretty decent coverage.
3. Bulbasaur. It sails through most Gyms, but it is terrible in the rival battles and against the E4. It only learns Grass and Normal type moves, giving it terrible coverage.
Yellow:
1. Pikachu. Duh.
G/S/C:
1. Totodile. A Totodile solo is so easy, the game isn't even fun anymore. Surf/Ice Punch/Return/Earthquake beats everything in the game.
2. Cyndaquil. Not as easy as Totodile, but Flamethrower(or Fire Punch at lower levels)/Thunder Punch/Eartquake/Return still beats everything with ease.
3. Chikorita. Not overly difficult like Bulbasaur, but not easy like Totodile either. With Tackle and Mud Slap it should be able to make it through the early game, with Return, Earthquake and probably Double Team it is able to make it through the late game as well.
R/S/E:
1. Torchic. Its typing is perfect. Because it takes much longer to reach the first Gym in this game than the others, it should have evolved by that time. And with Fire/Fighting STAB it rips through the Gyms and the E4. Wallace's Gyarados in Emerald might give it some problems, but I think he will be enough overlevelled by that point to KO it with Return.
2. Mudkip. Nothing can really hurt it, while STAB Surf and Earthquake hurt plenty of stuf back. With Ice Beam and Return for coverage it won't really have any trouble.
3. Treecko. Treecko still makes the game easy. Unlike Bulbasaur and Chikorita, Treecko actually has a movepool bigger than Grass/Normal(/Ground). With Dragon Claw, Brick Break, Iron Tail or Aerial Ace as possible fourth moves, I don't think there is much that it will have trouble with.
Fr/Lg
1. Squirtle. Not much has really changed for Squirtle. It is still able to use Surf/Ice Beam/Earthquake and slaughter everything in its path.
2. Charmander. With Metal Claw to beat Brock and Dragon Claw to cover Lance's Dragonite, everything has only gotten easier for Charmander.
3. Venusaur. At least he learns Earthquake and Sludge Bomb now. But with Gengar now having Levitate, that still doesn't help much.
D/P/P:
1. Chimchar. Torchic, but faster and with better moves. Even easier to beat the game with than Totodile.
2. Turtwig. STAB Wood Hammer and Earthquake with Stone Edge for coverage is nice. Torterra doesn't have the raw power of Infernape, but it still rips through the game.
3. Piplup. Steel isn't too good as an offensive type. With Surf/Ice Beam/Earthquake it is still able to get through the game just fine, but not as easily as Infernape or Torterra.
I don't know about Hg/Ss yet. Especially with the Elemental Punch TM's being removed and the physical/special split there could be some differences. But I still think it is 1. Totodile, 2. Cyndaquil and 3. Chikorita.
If you don't do a solo, it doesn't matter which starter you use. The other members of your team are more important.