I don't think age really has anything to do with it- it's more about experience and skill (and of course, the financial ability to support a horse!) Clearly, anyone who's still living with/supported by their parents has to get their buy-in as well.
I think you should be to the point where you're capable of identifying and correcting bad behavior on the ground and improving the horse with each ride under saddle before purchasing a horse. Horses can be very good at pushing the boundaries to see where they are, and too often inexperienced riders let the horse get away with small bad behaviors because it's cute and then find themselves with a horse that doesn't respect them. This can be a potentially dangerous situation. Under saddle, I'm definitely of the opinion that every rider is a trainer. Absolute beginners just don't know how or what to do to develop a horse to be better. But eventually they start to build that knowledge and learn to push the horse to do more difficult things, respond promptly to their cues, etc.
Leasing is a great idea for easing into horse ownership. I half leased several horses while I was learning, but before I bought I did a full lease as kind of a "trial run" to buying a horse. I leased the horse in from off-site and moved him to my barn, was responsible for scheduling the vet and farrier, caring for him when he got an abscess, etc. I really did know after that what I was getting into after that, and I had ridden enough horses to know what I was looking for in my horse.