I would buy some very general items that can be used on other horses you might own or lease in the future. I would (personally) stay away from the saddle as others have mentioned. That being said, if you do choose to buy a saddle, you might look into a nice ( lower priced ) used saddle that you can either re-sell, or just hang-on-to. Also, make sure the saddle you buy is fitted properly & approved by the owner of the horse.
Items that you could buy, that aren't TOO expensive ( and a bit easier to use on multiple horses) include bridles, bits, rugs, saddle pads, shampoos, first-aid items, sprays, fly masks & other accessories, grooming supplies, halters & leads, leather cleaner, stall signs ( in-expensive, but more custom). You can also think about buying some carrying cases, such as grooming bags, saddle covers, bridle or helmet bags, etc.
As for blankets, you could buy a few fun coolers or show sheets. Some blankets can be quite expensive, so if she has her own, I would just use those.
Hope that helps!
" If the entire world was one big machine, I couldn't be an extra part. I had to be here for some reason." ~ Hugo Cabret