I hired a horse for my first hunt from Hunter’s Rest, had a great experience. If you are hiring a horse from a place like that where they are accustomed to bringing out newbie foxhunters, they will have all the tack for you. Just bring yourself and be ready to groom and tack up. Some places, though (like Pleasant Prospect in MD, also a great place), will do all the prep for you if you pay for it. I did not hunt with PP, but at both places I had a chance to ride the horse before going on any kind of excursion. Generally the horse owner/barn manager will want to make sure you will be safe in company before turning you loose.
With other owners (I have borrowed horses from many!) it was more of an informal arrangement. For some I had to bring my own saddle, others had a saddle I could use. For these it was pretty much they told me when they needed to leave to get to the meet on time, and it was my responsibility to have the horse clean and ready to step on the trailer.
Probably the most challenging thing I encountered this fall (my first season hunting) was figuring out how to avoid getting my clothes super dirty pre-hunt. My magic formula: I prefer to arrive with all my hunting clothes on (except for jacket and tall boots). I have a jacket and sweatpants on top to keep clean while grooming my horse, and boots that I don’t mind getting dirty. Then at the last possible moment (less time to get dirty), I take off my top layers and switch to tall boots. I put on my hunting jacket last, after I unload the horse from the trailer.
Re: using a crop–certainly not a requirement, but you just need to use whatever aids you need to ride your horse safely and not be in other people’s way. If your legs and seat are all the aids you need, so much the better!