Let's see....

If you pick Bulbasaur you shouldn't have a problem beating Brock and Misty, plus you'll have resistance against Surge, Erika, and Koga (just beware Koga's exploding Koffings).  Sabrina and Blaine will be a bit of a problem, but by then you'll have something else to fight them with.  And of course, Venusaur can easily beat Giovanni.  However, you may find it a bit hard to use against the Elite Four.

If you pick Squirtle, you'll have no problem with Brock, and resistance against Misty.  Surge WILL be a problem unless you pick up a Geodude/Diglett.  And hopefully you'll have a Flying or Fire type for dealing with Erika.  Of course, Blaine and Giovanni won't be a problem, and if you teach it an Ice-type move, it'll be extremely useful in beating Lance later on.

If you pick Charmander, you'll likely need to find something for beating Brock (or train your Charmander to learn Metal Claw and evolve to Charmeleon), and you WILL need something else for Misty.  Erika won't be a problem (you'll likely have Flamethrower by then), but you'll probably need other things to beat the other Gym Leaders.  Fortunately, Charizard is capable of fighting in the Elite Four, as Flamethrower will bring down Lorelei's Jynx, a Flying-type move will bring down all of Bruno's Fighting types, and if you teach it Dragon Claw (found in Victory Road), it'll be useful against Lance (though you still want something with an Ice-type move for Dragonite)

Of course, it all comes down to which one YOU want to choose.  Can't wait to see how this run turns out!