I try to have the mini as close to what it's supposed to be, but i got a thousand of them so that's not generally hard to do. Sometimes i'll base an encounter around a mini just because it's a cool figure.
I own over 1.000$ worth of DDM minis, so I usually don't have problems finding a miniature which is similar to what I'm trying to depict (maybe a wolf instead of a hyena, or a bat instead of a stirge, things like that).
When I plan a campaign, however, I try to get the best miniatures I can, paint them and use them as "deluxe encounters". For example, I recently bought a bunch of Reaper gnolls to run the Legacy of Fire AP.
And if there's a mini I'm particularly fond of, I usually twist things a little bit in order to use it. My players are definitely encountering an owlbear instead of a dire boar in our next game