Hello, I thought I would reply since I am also (sort of) a first time horse owner. I have kept 2 horse at my house for almost 2 years now and many unexpected things happened. When you go to look at the horse take someone experienced (20+ years of experience is good). Decide what you want the horse for(hunter/jumper/reining/family/lessons). Fotr example, if you are looking for jumper you want a horse with long pastures (the muscles allow the horses to jump higher). Remember that keeping a horse if VERY exspensive. If you live somewhere grass is not availible all-year round, be ready to pay for hay in winter (and lug buckets of water to the barn too). You will want to find out if there are other horses in the area. Ask other horse owner who their vet is, but more importantly who their farrier/blacksmith is. **most blacksmiths won't come out for just 2 horses, thats why you should get on shedulae with the surrounding horse owners** another thing to look out for is stiffness, previous founder, and you probably won't want to buy a pregnant mare. Most horse owners will let you have a horse on trail, if you are really interested try and do this. Finally, when you find the horse you want put down a deposit (10% of the whole price is fair). This will insure you as the new owner of the horse.
there are alot of unexpected things, but you'll learn from your mistakes, I know I have! Good luck in your search
***remember, get the horse vet checked. this is very important***
good luck! :)