Hi and welcome to HF!
When looking for a new horse you need to take into consideration his temperment, personality, how he is to handle, groom, tack up, ride- out/jump/dressage/barrels/copmetitions? (whatever you want to do with him); is he good to shoe/catch/load/check teeth/vet visits; has he had any previous lameness and why; does he have any 'vices' like weaving, windsucking/cribbing (check his front teeth for signs of wsuckers/cribbers), box walking, etc.; Is the horse on medication or suplements for anything, what-why-since when-is it working...
Visit the horse a few times (meby add a suprise visit if you think he may be doped or whatever) before purchase and go through the motions with him (make sure the owner does stuff first just in case the horse is a nutter!!)-
-catch (does he move away or towards you in the field, buddy sour?)
-lead (bargy/lazy etc)
-groom (nippy or grumpy? lets you pick his feet up?)
-tack up (girthy? difficult to bit?)
-lunge if you want
-mount and ride in various places (spooky/ too forward/lazy etc do you enjoy the rides)
-hose down/bath (always useful to know it they dont mind the hose pipe!)
-feed (how are his manners?)
-lead back to field (again, manners)
When buying a horse the most important thing to consider is what you want from the horse. If you want a horse you can just hop on and go for a ride with minimal faff, a green broke 4 year old wont suit you. Or if you want a challenge or a horse to bring on and train yourself, a 15yr old school master wont fufill your needs.
Some people find their ideal horse first time they go out, others don't find them for several months of searching. And just out of interest how did you find him if you didn't find him in the 'normal' way? Just curious :) I didn't find Alli in the 'normal' way either!
Hope you have loads of fun with your new horse if you get him!!
We lose ourselves in the things we love, we find ourselves there too ~Kristen Martz