If your offering Vega as a Full Lease, 5 days, then the leasee should be paying everything! 100% of board, tax (why do
some places in NJ charge tax anyways?!? Never got that...?)farrier, vet, dental, et cetera.
I totally get what you say about not wanting them to train her, just make sure you approve of and get references for their trainer, and assert the fact that the trainer is at their own cost! And watch them BOTH work with Vega!
I think normally, and best case scenerio, is
you supply the horse's own tack. Mostly because then you know it fits her properly. There's no issue of ill-fitting tack and the chance of injury to either horse or rider. However, make sure you include a clause in your lease agreement about what tack is to be used and what isn't, and how the tack is to be treated (i.e...cleaned after every use) and stored, and that if it breaks it is THEIR responsibilty to fix or replace it. If you allow them to use their own, make sure you fit it to Vega first. And again, get in writing that you are not responsible for that person's tack should it break or get stolen, et cetera...
And personally, I don't like the idea of allowing a leasee to remove your horse from the property. I'm totally paranoid like that.

On different levels though...1.) Whose to say your horse will come back? And 2.) it opens up a whole new window of "Things that can go wrong and kill people and/or horse", yah know? IF YOU DO...make sure the leasee and horse are insured (which I'd insure your horse and yourself anyway...for the horse I would ask they pay half, if not all...With the insurance I ask partial because no matter what kind of lease, YOU are ultimately responsible for YOUR horse's health, yah know? You should always be checkin' up on her health and happiness). Also, if you do, again make sure it's written "at their own cost" for trailer or other fees.
I'd only allow removal (like showing opportunities) of your horse from your property after at least 6 months of continuous lease if you like and trust the person and the lease is working out 100% for all involved. I mean, unless you already know the person.
And I cannot stress enough, get absolutely
everything in writting and have numerous signed copies for every party involved, including your BO. Best way to avoid (God forbid) possible future problems!
G'luck! And if you know anyone up where you live, TJ's also still available. I'd be willing to move him to a closer facility as well. There's a few up your way I can look into.
Happy Holidays!!