If you are buying a showjumping horse check the results of the horse because most of the countries for example France has a data system for it. So you can understand if it is a stopper or injured etc. If you see a horse with good result for a year and dissapeared after that you cam guess that it had an injury etc. Find a reliable dealer, try the horse by yourself for sure, feeling changes everything. Control the xray and blood test for sure.
Make someone ride before you try and see the horses behaviour first. Good luck with it. As I am also a lawyer, I was dealing with selling problems so I can give you some advice if you have any trouble
Get the horse vetted. Put money aside to get the horse vetted so you know there are no problems. With no offense don't take the owners word as they will do any to sell.
And if you are going to be competitive check records at shows to see how the horse has placed.
Depends on your level, but if it's a horse that's going to be your next riding horse, make sure you're 100% comfortable with it while riding and handling.
Think about what you do at home and see if this horse will fit in the criteria - don't buy the first one you see, unless of course it IS actually perfect.
Check the conformation, is he even and straight, and sound! Whether you get a vet check or not you do not want to buy a lame horse. You're welcome to send me photos or I'm sure if you posted on forums, you can get loads of advice.
Temperament. Presuming you'll be viewing this horse at his home, he'll be comfortable and very used to the arena, so take not on his personality and general vibe. If he's spooking at something, he's probably going to be worse at a show, but if you don't care about spooking or he got over it really quickly and you want to pursue him then that's a risk you take.
When finding horses to look at, think outside the box, you may want say a hunter jumper, there may be a horse advertised as a dressage horse that can jump, which would more than likely be a perfect hunter jumper.
Dependant on the situation, you can get the owner/rider to ride first, or you can get on first, just ask and ask them 101 questions about the horse, how is he around feed? Aggressive in the paddock? How is he to catch? Unless of course you don't care about any of that.
You can also hire people/trainers to come with you.