Outside of a Nuzlocke or monotype or something like that, I don't have a "team" other than whoever I've got with me currently. I just never even considered playing the games that way, and it's only been slowly that I've come to realize that so many (most?) other people actually use a set team.
I rotate constantly. I go into each gym with a team that's assembled solely for the purpose of beating that gym, and I go through the routes with... whoever. For traveling, I just try to have a good range of types so there are no threats I can't work around, and if it comes down to a choice between two or more essentially equal pokemon and I don't have any particular preference, I generally go with the one with the lowest level, so it can get the experience. I generally work out of a pool of 20 - 30 pokemon - less early in the game, but more just as I catch more and so have more I want to try.
Over the course of the game, I come to know the pokemon, and to learn who's more or less dependable, and the "team" starts coming together. By the time I get to the E4, I've got a pretty good idea of who's best in each role, and that's pretty much who I take with me when I face them. The starter has been a part of that group... maybe half the time, if that.
The starter's no more special to me than a starter car in a racing game. I only rarely move it down into one of the rubbish boxes, since they tend to be at least better than average, but they're rarely anything really special, so more often than not, they don't make it on the final team.