If you've been taking lessons, the you're on the right track! I'd say, go for this new horse. You will know when/if you guys click. And know how that feels. When it comes time that you're ready to start looking for a horse, you have to explore allll your options and not just fall for the first one because he's "cute" or "well-behaved." Most horses are very different when you bring them home. You have to be absolutely sure that he's the horse for you.
Why did the lease not work because you were sick? Could you not get out to ride him, or what? These are things you have to think about when considering buying your own horse. Who will feed your horse if you are unable to be there, become sick, etc.? Will your parents or a friend be willing to do it for you? Also, would the trainer at your lesson barn be able to help if you had a question about your horse's care? Or a horsey (adult) friend? You have to have ample resources and knowledge to responsibly care for a horse.