Personally, I would lease first. Being as you have only been riding for two years, you may want to switch disciplines or stop completely. Either way as you mature as a rider you will begin to need a more mature horse. I recently purchased my first horse (about 11 months ago now) and it was the best decision of my life! He has taught me so much and it is great learning so many things from your horse and understanding what that horse is like in all situations!
(Also, it is a huge step from riding lesson horses/ponies to buying your own. So either way I recommend leasing a horse first to see if that is what you really want. They are a lot of work and time! I know everyone says that but it’s completely true! I have been riding since I was 3 and leased countless horses, however there is such a huge difference even between leasing and buying, but leasing is that step you need.)