Probably the most classic furry persona I have is a fox anthro named Morriganus Redleaf, he's sort of an unwilling dimensional traveler I came up with one day for a virtual bar RP. His home dimension is a sort of fairy realm of permanent twilight where the stars are always visible, and it's lit by several moons and one low-intensity sun.
One character in a sort of furry vein is a young man possessed by the spirit of a supernatural Tigress, which he gets a number of powers from, including shapeshifting.
Mundane animals I like are mainly birds of prey, hoses, wolves, and cats. bear is sort of a new one. I was really close to Orcas when I was younger, but not so much anymore. Extinct animals I like are sabertooth tigers and Utahraptors (think the velociraptors from jurassic park in size, since real velociraptors were about the size of a small dog

)
I love dragons and gryphons, and tiger-form Rakshasas from indian mythology (Vibhishana is one of my favorite mythical characters.) I like centaurs too, especially since that's my zodiac sign.
Little bit of everything, really. It changes based on my moods, kind of just a make believe for fun thing. In some aspects I see it as energy work, connecting with the energy of whatever animal I should learn from at the moment.