$450 seems really cheap to me. I live in NY and you can't find a decent horse for under $1500. I know your looking for a good deal, but buying a pricier horse may save you money in the long run. I live near a large ranch which sells and leases thousands of horses each year and allows you to make trade if your particular horse doesn't work out for you. I would try to find a place like this, or try leasing a horse for a summer so you can see how everything goes without first committing. Taking lessons before buying is another way to help you build skills and knowledge and will help you later when it comes to choosing the right horse.
For a beginner I recommend a gelding between the ages of 10 and 15, anything younger may have a little too much spunk. Older horses typically are better behaved but you have to think about how much time you will have with them before they are retired. A horse can be used for trail riding up into its late 20s. The breed I recommend is the quarter horse because they are more even tempered, Paints, arabians, thouroughbreds and appaloosas tend to be a little spirited and may be difficult for a beginner although htere is always variation.
Since you are inexperienced, I would find someone you can trust who is an experienced horseman/horsewomen who can check him out for you and to see how he rides. Make sure that you canter with him because if any problems are to occur with a horse it will happen at higher speeds. Apps are known for their attitude and can be difficult for a beginner, but some make great companions. Also check his eyes for any cloudiness. Apps are susceptible to an eye disease called recurent uveitis which can get expensive treating. Check his feet as the others have suggested, a horses entire health and well being are dependent on its feet.
I know I sound scary but I just want to help you out making a good decision. I too am in the process of looking for a horse. I have been riding for years and enjoy the sport of team penning and rode my friends' horses all summer in competition. Helmstead has made some great points. I suggest you look into things more and build your skills and knowledge before making a purchase. A hasty decision could cause you to unneeded stress and financial burden.