And.. When going to look at a horse, show up early, maybe 30 minutes or so. If they're in a pasture, you get the chance to see how easy (or not) they are to catch, how they react to other horses, if they're with any, and the owner wouldn't have the chance to down 'em (it's not as common as you hear, but it does happen)
Also, if the horse is "rideable" be sure to get in a ride or two, but not before the seller hops on first. I have a friend who went to look at a mare that was "safe" and she asked the seller to ride first. The mare started bucking before she got her bum in the seat.
Be sure to keep a helmet around when riding a horse you've never ridden or haven't ridden much (most of the western riders I know don't keep helmets around because "they're for the English snobs" and "they're useless") I keep on in my car, and one in my barn, even though I haven't been able to ride in two years.
And if possible.. Take a few trips to see said horses before making a decision rather than just going by one visit. Like people.. Every day is different. Try to get as many views on their personality as you can before you end up with a moody mare or cranky gelding you're not ready for. (I'm only assuming you wouldn't get a stallion for your first, but the same applies to them)
Carpe diem sine desiderio, et ad vitam vivere summum