I 100% agree with everything Ondine said but also just take a moment and really feel how the horse feels with you. Never rush into anything, you'll know when it's your perfect horse. Also see if the horse is available for trial so if you do end up really likening it you can take him for about 5 days and see how he works in your environment.
Question to ask:
Do you know how many owners the horse had before you got it?
What kind of a diet is the horse in at the moment?
Is it an easy keeper ? (Means does it keep its weight on a constant level)
Has the horse had any injuries?
Can you take the horse out in his own for outrides?
Hey 👋🏼 I am not sure where you are based or where you are going to try the horse but I am in the UK and these are the things I look for: horses health is the most important thing to me so I will normally check over myself at first viewing( you can look at YouTube videos on what to look for) and if I decide to go through with the horse my vet will come and do a full check over before I buy. If the owners trying and talk you out of a vet check then think why? Next I would look at the horse as a whole and look at how they move is he suitable for what I am wanting to do? ( jumping, dressage, showing) You need to make sure your comfortable riding the horse.
I would be looking at the horses environment are they happy?
Things to ask:
Ask about the horses history so health history and competition history.
Ask to see the horses documents. Also if they say the horse has winnings or points from competition (Eventing/ Showjumping or Dressage) I would ask to see proof of this as many times the horse doesn't have these but by saying the do the can often increase sale price.
If you are considering buying then I would ask some more questions just for the care of the horse so can he be in a mixed heard(mare and geldings)? Also what are feeding him at the moment. When buying a horse no question is silly you need to know all the information! Best of luck and hopefully you have a new horse soon!