I also think that you're ready.
Leasing a horse isn't rocket science--even if you end up with one that isn't for you, most lease contracts are quite forgiving, and you can back out after 30 days. Provided this is all detailed in your contract, it takes out all the difficult parts of owning a horse: there will be no unforeseen expenses, there are no 'required' purchases, you won't have to deal extensively with barn management, etcetc. You get to enjoy a horse on your set days, and that's that.
I will also counter
Arabian's point, with a caveat. We don't know all that much about your situation, but if you're getting one lesson a week, a part lease will double or triple your riding time. So, with this in mind, I'd go with the lease.
However, if you can get one or two more lessons a week, or if you have free access to lesson horses (I always did as a teenager), then it's sort of 'half dozen in one, six in the other', and Dreamcatcher makes a valid point.