You've got some good advice there, including the bit about whether there's an option to buy. I'd say, make sure that you and the horse *like* each other as well. I don't mean Unicorn and Rainbow Love, but if this is a horse that is interested in you, and willing for you, and you like his personality, that's important. No sense in getting into a relationship with a horse where you're going to rub each other the wrong way all the time.
Enjoy the half-lease! It's a great way to get your feet wet on horse ownership!