Nearly everything you need to have a horse.
Saddle, girt, bridle, saddle pads, halter, lead role, leg protection, blankets, cooler, fly sheet, fly spray, grooming tools, first aid kit, and of course feed and shelter for the horse. You will also need the proper riding supplies. There are other things you may find you need to purchase including clippers or a breast collar.
Have it's body condition in mind for feed so you know what to give him.You probably won't need tack (saddles,bridles, girths,etc.) because you could borrow something from friends or your trainer.You will bandages,ointment,gauze,etc. incase there is an accident.Also I would recommend getting a halter and lead rope so you can get your horse from the pasture or stall.If your horse is sensitive to flys you could get him a fly sheet,if it is cold you could get him a blanket.If you don't already have grooming tools you could get him some.Fly Spray,Liniment,Detangler and other sprays or creams are optional. Hopefully this helped! Good luck on finding a horse!
Lights sheet/ stable sheet
That is really all you need when they first arrive. Once you get to know them you can go out and get them more stuff (riding stuff).
A first aid kit. This is a must have for every barn. You can find lists online of what to include, but you should have, at minimum, a couple different antibiotics (I have a spray on one and a salve), vet wrap, fly repellant salve for wounds, scissors to cut bandages off, non stick gauze, and a stethoscope and thermometer for checking your horse's vitals.
Other things to consider: fly spray, hoof oil, duct tape (!!!), and grooming supplies.
This is a bit off topic, but I would also suggest familiarizing yourself with your horse's normal behavior, recording his vitals (heart rate, respiration, temp, gut sounds, and capillary refill time), and keeping your vet's contact information in your first aid kit.
Make sure you have basic feed and things for the stable like water buckets and bedding. Also have a grooming kit and washing things. Hope this is helpful
Before it's hard to buy something because probably you don't know well the horse and his details (like measures, ..) you can do a list of everything you don't have for the horse and then when you have him, you take all the details together and you're gonna buy the right things
(Saddle, bridle, blankets, protections, care products)