You'd get a zorse. Looks, to me, kinda cute but what in the heck would you do with it? You might need special permits so I'd check your state and county. I don't believe they're particularly easy to train. They are also unbelievably expensive.
I know a gal who dabbles in horsetraining and colt starting who did some work on a Zorse. She rode him just like a horse, English and Western, and he did really well. He was really pretty, sort of a dusty dun color with faint stripes all over, except his head, and a little darker striping over his hips and down his legs. His mane grew straight up, just like a zebra. He got along well with their other horses and animals, and she never had a training issue with him beyond what a normal young horse does.
I saw a zorse for sale for $1000 once actually. I don't think it had been started, but still. I think they had some at the Cal Expo auction when I went too..Not as pricey as you'd think. And I've also heard that usually they're pretty similar to horses as far as training goes.