Uh, to start out with my list would look something like:

Body brush
Hair brush (for mane and tail)
Curry
Hoof pick
Buckets (though really, I wasn't required to buy my own as the barn supplies buckets. But I did get Kieran his own water bucket and his own feed tub)
First aid (though again, the barn pretty much has this covered, I'd get this if I was elsewhere, or keeping my horse on my own)
Definitely two halters and leads (preferably at least 8 feet long)
Bridle, reins bit
Saddle, girth/cinch, saddle pad (or two).

A lot of the other stuff on your list don't jump out to me as immediate necessities. I'd also make sure she doesn't just go out and buy any old saddle but ensure she gets one that fits the horse (and her). Don't just base saddle size off whatever the lesson barn has been using either, they don't always spend a lot of time ensuring really good fit.

And if she's riding English, she'll also need stirrup irons and leathers.

As far as where to buy stuff...I buy a lot online, usually Horseloverz when there's a good sale and I can get free shipping. (I've gotten halters and reins for $5 each, lead ropes for a couple dollars, stirrup irons for under $20, saddle pads for $5...you get the idea)

I also love to browse my local tack shops' consignment sections, you can get awesome deals there too (like my mattes half pad, lightly used, for $75).

And if you have any auctions near you to do tack, that is a GREAT way to get supplies and tack for cheap. I got a nice Simco saddle there for $200 (of course, it didn't end up fitting my horse but I was able to turn right around and resell it to a friend), side reins for under $10, western saddle pads for a couple bucks, split reins for $1. I'm totally serious.

Also: see my dollar store thread I posted today for other ideas of horse-related stuff cheap.