When you decide to take lessons my biggest suggestion is to find a place willing to teach you from the ground up. I mean a place that is will to teach you every inch of basic horse care prior to ever riding. Owning a horse is so much more involved than riding. Please do not take this as a rant I am speaking from personal experience. Riding will literally be a very minute part of horse ownership. That being said I think you are on the right track wanting to lease prior to purchasing. As far as a budget goes.. the cheapest part of owning a horse is when you buy it. All the million and one little things add up fast. There is truly no such thing as a free horse. As far as items you could prepurchase.. the obvious items would be your basic grooming tools,feed buckets,scoops, scales,feed bins,leads,lunge lines,crop,etc. Items that do not need to be fitted onto your horse. Are you planning to board when you purchase or have it on your own property? If planning to have it on your own property you have fencing to decide on.. which can be a very large and expensive decision,housing, screws,posts and I mean these as extras aside from what you install because inevitably something will break and I prefer to have replacement items on hand. DO not forget eye bolts,hose pipes, water troughs, bedding,manure rakes,wheel barrows or in my case the dumping poop wagon(so much easier for me to move and dump), regular leaf rakes and so much more. Also keep in mind that one is none and 2 is one. I have a double set of grooming supplies for my horses because I never know when one of the kids is going to misplace one. Making a basic list is really hard to do lol. The dollar signs will keep racking up. Not trying to scare you just wanting to give an honest view on it.