Ability and Price
Always have a fixed price limit in mind. Every week there are thousands of horses advertized for sale, and invariably it will be the one just outside your price range that sounds perfect.
You should not even consider going to look at a horse if it is outside your price bracket, but it is always worth asking the seller if they are open to offer.
As mentioned, it is a good idea to buy a horse that has done more than you have and that you can learn from.
However, once again, it is a matter of common sense to judge whether a horse has too much ability and scope for an inexperienced or novice rider.