While I don't use miniatures any more, back when I was a kid playing D&D, we did, at least for marching order.
Back then, we'd pick a miniature and then base a character around it. I remember one character that drove my DM crazy, I thought it looked like he had a toad on his helmet. So I kept pushing for him to have a toad familiar. And my DM (rightfully in retrospect) said it was just a horse ornament (I guess maybe it was a Rohan inspired figure).
Anyway, Hero Forge allows you to make your own custom figure. Pretty neat. (They seem to be overloaded right now, takes a while to load)