Don't get emotionally attached to the prospective horse. It'll cloud your judgment and you might end up buying a completely unsuitable horse or make it that much harder to walk away if the horse isn't right for you.
Don't buy any horse without a pre-purchase exam.
Don't buy a horse you've only looked at once.
Ironically, I've made the mistake of doing all three of those. :?
Yes do not get emotionally attached to the horse. Oh also be leary of sellers who won't consider a trial period, even if it's for three days if they are confident that the horse is well behaved and "BEGINNER SAFE" as they advertised ( you can tell I had this experience) then why worry as long as you assume the risk to purchase it if you injure the horse or something happens.
Don't buy after first look, visit horse and ride it atleast 4-5 times, in morning, in afternoon, in evening if lighting permits. walk horse around all three times on lead to see if they drag you around the property or are pushy, etc and groom each time and tack up to see if they are sensitive to things or crazy in crossties, etc. Also, riding in new place will tell you if they are a freak out of their comfort zone or if they have a reasonable mind and how big they spook if they do, things you need to know that you won't see at their comfort zone. but ride ride ride to see how adjustable they are and how respectful they are of their rider.
Again, I didn't have the option with my first horse and the no buck, no rear, no spook, no bolt beginner safe horse they advertised ended up doing all four things on me after the first week. Too late I already gave them my money and was stuck for 3 months with an impossible horse that was not a good match for me. He was a dream at his barn but once moved to a new location his real side came out..dominant, disrespectful, high strung and dangerous for a beginner. We joke that the drugs must have worn off but really should have pulled blood on him at PPE.