I look first in the miniature collection I already have - I have an interesting variety, and they are all figures I like (or I wouldn't have bought them) - and most (2/3 or more) are unpainted. Then I take the one I like (or I buy one if I can't find one in my collection) and I paint it to match my character concept.
Occasionally I'll find I already have painted a figure that fits the character and I'll use that one, but it is more satisfying to paint it custom-made. That allows for some interesting little character-flourish details.
Some of my players have also done that, either bought their own figures, or found one of mine they'd like to use, and I'll paint them for them (though I'll keep the figure if it is mine).