I've only ever played the first two generations, so here are my favorites for them.
For Red/Blue version, I chose Charmander first. Yeah, the first two gym fights were a *****, but everything was smooth sailing after that. I unintentionally found out that a high level Charizard is indestructible; I would only train him on my first play through, and he was over 70 by the time I got to the Elite 4. (I also caught Mewtwo with a standard pokeball after almost one-shotting him with Charizard, neener neener neener.)
As for Gold/Silver, I chose Totodile. As it turns out, Feraligatr is also freaking powerful and awesome.