Okay mine will probably sound lame, but it’s stuff you will always need and sometimes need multiple of.
Brass double ended snaps and bucket straps. These are things you won’t think you need until you do, and then you won’t be able to find any when you desperately need them. Riding Warehouse has brass double ended snaps for like $2.
Big plastic dosing syringes. I am a dosing syringe fiend. You can never have too many. I love the 60CC catheter tip ones from Smartpak (brand is Monoject.) They’re under $3.
Duct tape AND Gorilla tape.
Towels. Many towels. Hand towels, medium towels, large towels. Buy all the towels.
Rain coat and rubber boots.
Farrier kit. A small rasp, nail pullers, hoof testers, nippers, and the clincher tool (IDK what it’s actually called.) Nothing more frustrating than having a sprung shoe and no way to take it off because there are no farrier tools available.
First aid supplies. Thermometer, the old school non digital kind. The fast digital ones are great until they lose accuracy or the battery dies. The classic kind is reliable 100% of the time. Pillow wraps/standing wraps. Wound cream (there are a zillion.) Cotton roll. Elastikon. Vet wrap. Brown gauze. Gauze pads. Vaseline. Regular scissors. Bandage scissors. Another pair of regular scissors. Betadine scrub. Latex or vinyl gloves. Brown Listerine. The list goes on and on.
Bathing supplies. Buckets, shampoo, sponges, bathing mitts, sweat scrapers.
Extra halter and lead rope. Either all leather halter or nylon with a leather breakaway crown piece.
Okay that’s all the crummy boring stuff that isn’t exciting to buy (unless you’re a weirdo like me.)
Fun stuff you’d want ASAP are a set of blankets (I’m assuming he’s already being blanketed by his previous owner?). A sheet, a medium, and a heavy. There are a lot of good deals going on right now for blankets and sheets.
For grooming, I am a big fan of the Winners Circle brushes. I have some that are older than my current horse, if you take care of them they last FOREVER, and the natural bristles are a lot nicer than the plastic/synthetic brushes. Hoof picks and hoof brushes as well. I love the Ultimate Hoof Pick. Is it stupid expensive? Yes. Is it the best hoof pick of all time? YES. After using it, all others will feel inferior and inadequate. Really helpful for getting ice balls out of their feet too.
Another product that’s helpful and fun are the Premier Equine quick wraps. Think BOT Quick Wraps but a fraction of the price and you can get a variety of interchangeable wraps (ceramic, magnetic, regular.) I use these for hauling and omgosh they have been a life changer. So much faster than regular wraps, especially at the end of a long show day when you’re tired and just want to go home.
Fly gear (mask, fly sheet, boots.) A lot of stuff is on sale right now. It keeps them a lot more comfortable in the heat and the bugs, and they stay a lot cleaner too.