I used to work for an opera company, so I got a crash course in vocal types. My two favorite operatic voices are Countertenors (the guys who can sing really, really high) and Mezzo-Sopranos/Contraltos (the girls who can sing really, really low.)
Here’s a couple samples. First, the amazing Anthony Roth Costanzo, a Countertenor:
And here is Mezzo Joyce DiDonato:
As for non-opera, I do love vocalists with distinctive styles. One of my favorites, and I know won’t be to everyone’s taste, is David Thomas of Pere Ubu:
No option for “some of the above,” but that would be my answer. My favorite singers tend to be near-flawless and beautiful (the late Sandy Denny is my absolute fave), but I like lots of weird singers too, and several twangy/country singers are on my list too. Easier to say what kind of voices I don’t like: thin little waifish ones, and ones who can’t stay on key.