it sounds like leasing is such a good idea for you! it really depends on the type of lease and individual agreements on cost and things like that. half and full leases i feel are the most common. if you half lease with someone, it could either be the owner of the horse or someone else.. make sure you like the person you half lease with, ive seen things go wrong one too many times with the leasees not getting along!
here is an example of each:
my one friend have leases for the year with someone else, she pays half of everything.. $250 for board, $55 for farrier, half of the cost of shots, injections, ect. she does buy the horse things such as halters, leadropes, and saddle pads, and other small things like that, and uses her own saddle. she will be keeping all of these things once the lease is over. she also pays for any lessons and horse shows she decides to do. she has a lesson once a week and just rides another two days a week.
my other friend full leases and she had to pay a cost upfront. then she pays the whole cost of board ($500 a month), all vet, farrier, insurance, and any other costs. she also uses all of her own tack, blankets, brushes, and other things for the horse, but will be keeping them once the lease is over. the horse is at the farm of her choice and she gets to ride, lesson, horse show, ect. as much as she wants.
if you only half lease with someone thats on the property, then you can just continue to use all of there brushes, tack, and other things for the horse. i have found that it really just depends on the individual situation. i would go through your instructor to find the best horse and situation for you to lease. you can be open and honest with her about how much you wish to spend and how often you want to ride. and she will know what type of horse you need.