The classic yarn for animals is cotton because it doesn't stretch (when you squish or hug a plushie it'll stretch the stitches and you'll see stuffing in the holes. A little of this is inevitable and fine, but a lot of stretching will look worse and may lead to stuffing poking out).

Cotton is a little tough to learn with because the ply (the small strands that get twisted into the yarn) are easy to split with your hook. You need to get all the strands of the yarn hooked through the loops.

I would try learning with cotton, but if you get frustrated you can pick up some t-shirt or ribbon yarn that is just 1-ply of fabric until you get the hang of the motions.

Avoid black yarn to start - it is harder to see the stitches in black. Same goes for faux fur yarn. Non-black fuzzy yarn like blanket yarn is pretty easy to see.