Sorry for the double post, just saw the other question. I use Brookside probiotics from valley vet, similar to Fastrack but easier to find. I'm using Grand Coat supplement now, as it has Omega 3's and zinc and copper, which are common deficiencies, with good results. Horse Journal, which does impartial reviews of various products for horses (kind of like a "Good Housekeeping Seal of Approval" or "Consumer's Reports" reviews) recommends this product as their Editor's Choice 2008 Command Coat and Hoof Brookside (Supplements - Skin Coat)
. It doesn't say how much Vitamin A is in there, but you could put a small extra dose of liquid vitamin A on the feed to supplement. FYI - the liquid is an injectable but Roadyy is right, it's not generally actually injectjed with a needle as it leaves big lumps for horses. It works better for horses to dribble it onto their feed and let them take it orally.
Great questions about what to look for. I agree with all of Roadyy's great suggestions. I would add that I would lead the horse around, tap its barrel to see if it moves away (laterally) from pressure there, and also walk toward its head and shoulder (e.g., do a right hand turn toward the horse) to see how well it moves away, with you, to stay out of your 'bubble'. I would do something like the pebbles in the bottle to see how the horse reacts to surprise, and then observe whether the horse 'settles itself' and how long it takes. I would also find something that it doesn't want to do, and use the natural horsemanship tools of approach and retreat to see how long it took for the horse to accept/perform the behavior. You could use that with the pebbles in the bottle -- shake it, horse is startled, calms down, and then try to do it closer to the horse's head to see if he accepts it. Use the approach and retreat to learn how the horse decides to trust you (or not) and accept the rattling bottle closer to his body.
If the horse is thin, be aware that he may not behave the same way as if he were fitted out and conditioned. He may be very mellow compared to what he will be like when he's home with you and well-fed. They get new, energetic personalities when they're feeling good.