To me, with the language you are using, it sounds like what you really want to do is sell this horse. There's no shame in that. Advertise him as a good trail horse as well as a cheap project and I'm sure people will be interested.
It sounds to me like you have too much horse. Remember that green+green=black and blue.
You stated that you only see the horse once a week. To me that is not enough to bound with a horse, train it, get it to a better weight, etc. Someone correct me if I'm wrong as I have never trained a horse before.
When you sell the horse, I would take LESSONS. Lots and lots of LESSONS. Even if it was just for the amount of time you currently ride...once a week. You said that your main goal right now is to gain confidence and something else I forgot. There's nothing for gaining confidence like a GOOD, friendly barn and an old schoolmaster.
Once you have a good amount of experience with lessons, move on to a lease. After that, evaluate where you are and decide TRUTHFULLY if you are not confident enough to own a horse at that point in time or if you want to continue leasing/lessons until x time.
Good luck and I hope you make a decision you and your horse can be happy with.