New World tarantulas have urticating hairs, and if you have sensitive skin, I'd probably pass, even if you don't handle them at all. Arthropods in general are very easy to develop contact allergies to.

Old World tarantulas do not have urticating hairs, but they are strictly look-don't-touch pets, and tend to be significantly more venomous (won't kill you unless you're allergic, but can make you very sick. And they don't have that first line of defense, so tend to be more tetchy).