As a seller and buyer I'm always asking loads of questions
My number one recommendation is to see the horse in flesh. Buying sight unseen is great for me if I want that unbroken 3 yr old that has a nice canter, but if you're buying a trained horse that you want a particular way, the only way you'll know what it's like is to go visit him in person. But if you do choose to go that way, as ducky1234 said, lots and lots of videos of someone riding him.
To see how hot they are you could ask questions like, does he need a whip or spurring to get him going, will he get faster if you drop the reins when riding trot or canter, is he spooky, does he jigjog/trot on the spot, how sensitive is he to your leg?
When people call me up asking about my horses for sale I get the general questions of how's his Health, temperament, and hooves are. Also when were his teeth done and if he's up to date with vaccines and worming.
I then ask who's he for and what will they be wanting to do with it, or, they will tell me this before I ask which is nice.
I've told a few people he doesn't sound suitable and they've come to view him anyway, which I'm fine with as I want the perfect rider for my horse, not a quick sale, every time, they agree, not suitable, but once I was wrong. I'm saying that because sometimes words don't get across right and things aren't always as they seem. (I was selling a OTTB, and it was for a 10y/o, but she rode him perfectly and tested him and now they're jumping 1m rounds)
I tell people everything about my horses, good and bad, I rather a bit longer phone call then waste a few hours of my time if they come ride. I usually get a lot of naughty horses to re-train and I'll tell the viewer that they used to be a bucker etc. telling people this has never turned anyone away surprisingly!
I'm going off track - but above answers have great questions and considerations.
I don't know your level of riding but my final thing is that if you're not 101% confident around that horse right there and then when you go see it, then chances are that you won't be for a very long time, if ever. Make sure you walk trot and canter, and push all the buttons you know, and if you feel like you could do anything with this horse then it's the horse for you, but if you're scared to canter it, it's not for you.
- - Without horses, my house would be clean, my wallet would be full, but my heart would be empty - -