I have been warned about Craigslist (at least in our area, Kentucky) by several people who know horses well. They suggest you use the main horse-sale sites like Horsetopia, EquineNow and dreamhorse instead. The problem is it is too easy to pop an ad on CL, and it has turned into the site for off-loading horses with issues and there are a lot of unscrupulous sellers on there.
As several folks have said, be ABSOLUTELY sure to get a vet check done as a condition of purchase, and my very strong suggestion is to get a trial period where you can spend time with the horse in your environment and see how you get along and if the horse has any issues. With a trial period there is usually a deposit that will not be refunded if the horse is not acceptable to you for certain reasons (you don't mesh, it doesn't get along with your dog, etc.), but that's a lot cheaper than buying an unacceptable horse. Make sure your trial period paperwork specifies you get your deposit back if the horse fails the vet check for specific reasons (problematic diseases, past injuries affecting riding, etc.).
Above all, else, good luck!! It is exciting to be on the lookout for a horse! I hope you find a really good one you will enjoy.