I mostly DM, so take all of this with a grain of salt.
My first character was the sample fighter who fights Bargle in the Red Boxed Basic Set. Good times. No impact, really. My first batch of characters after that were fighters, but my first big deal character was a Magic-User.
After that, I got addicted to thieves in 2e, and then thief/magic-users.
With 3rd ed, while I've dallied with them, I have no desire to play rogues or arcane casters anymore. I've fallen in love with paladins and clerics. I just can't get enough of buffing, going to town with a greatsword, and then healing whoever needs it. Maybe I'll get burnt out and go exclusively monks (but as I currently detest the class, this seems unlikely).
Any carryover from my first character? I voted "no." I still prefer good aligned characters and humans, but I'm not sure that's due to Red Boxed Set.