First rule of thumb, do you like the horse. You said you have been riding for 4 or 5 years and have begun running barrels. Let the knowledge you have guide you. Ask if they have any known bad habits, why did the previous owners let her go and get in this condition? If she has been used as a cutting horse, she is going to turn quick, will she bend around a barrel. Looking at a horse that is under weight can be an advantage as you can see defects easier. A fat horse can hide a lot of problems. You do want to know if they load, how they are for worming and shots, you don't need really to ask about temperment as you can tell when you approach them how YOU will get along with them, if you see any bumps or scars on the legs ask about them, ask how she is with a shoer. Mostly ask yourself, can I work as one with this horse.
Got a horse, got a dog, got God, got enough.