I usually encourage my players (I seem to have landed in the 'DM' bubble for a while now) to imagine their character before they start, and then, when they roll up their stats, adjust if need be (for example, you planned for your Wizard to be absent-minded, but your lowest roll is actually still an okay Wisdom score - just re-imagine a little to suit his new decent skills).

However, for my partner, who's somewhat judgmental of her own creative abilities when it comes to characters, first we roll up stats and THEN she creates a character around them - essentially using them stats as an initial canvas, which can work as a good booster.

As for not choosing something because it'd be 'out of character', or choosing a less than optimal feature because it fits character?
I do it all the time. It can lead to some great jokes if it all works out well (in 3.5 I played a character who was basically Aquaman... By accident. Oh, the hilarity).
On the otherhand, it may have led to the various deaths of those characters, but oh well, that's part of their story.
The risk here is pissing off your party for being 'sub-optimal', but in that, just try to be as useful as possible (I mean, your hero doesn't WANT to be useless, does he?) and not get in other people's ways, and usually you'll be able to have all the character-based creation fun you want.