I bought a saddle pretty early on in my leasing life. I WANTED a saddle, and I had to have one. It fit many horses, not all, but I got a lot of use and satisfaction out of it, so don't be shy about that. To own a saddle is a very distant , but undeniable, second to owning the horse itself. AND, knowing what saddle fits your lease horse, you can even look for the same make or size, used. Budget 400$ for that or a bit more.
Bridle is nice. Get a really good bit $150 to 200, and get good leather reins.
Grooming tools? Ang! Use the barns. There is no romance in grooming tools, unless you have small hands and the barns are uncomfortably large. Then get ones that fit you.
Good boots and Half Chaps! Tall boots are very price, but half chaps work like tall boots and are much cheaper. Half chaps $50 to 100
Breeches. I love full seat leather, but that's me. $85 to 120
Saddle pad and girth $140