Horses are expensive, I'll say right off. Just the yearly costs runs at LEAST a few hundred: Teeth floating (at least once per year), farrier(every 8 weeks), vaccines(every spring), wormer(every 3 months). It all varies by area but that'll run you a few hundred at least. If you have shoes, your farrier call will be more expensive.
*Minimum* supplies: Halter, lead rope, hoof pick, fly spray, curry comb, brush, mane comb, shampoos for washing, maybe a fly mask or fly sheet. If you're going to be riding, at at least a saddle (a good saddle will run you at least $400), bridle, bit, reins, saddle pad. These are just minimum supplies, keep in mind. You'll need a stock of money in case the horse needs a vet, which WILL happen eventually, as horses are walking disasters waiting to happen. There's tons of other supplies that she'll probably end up getting, because that's how horse people are (haha). If she'll be taking lessons or have a trainer, that too.
Boarding will run between 200 and 500 per month, depending on what you get. Most horses are find with pasture board, which is cheapest. Comes with pasture, hay, water. The basics they need - that's what my horse gets, and it's $215 for board per month.
When you're buying, you'll need to bring a vet out to do a prepurchase exam, so there's no hiddne health issues, and a Coggins. You want ot see a healthy, calm horse, and no ribs. There's a conformation guide floating around here - you don't want a conformational wreck of an animal. A solid trail horse will be more expensive, but they'll be calm, shouldn't hesitate when being lead, ride smoothly, be okay with being out by themselves.
Be wary of people giving out free horses. Be wary of someone who says you have to give warning before looking at the horse (call me 20 minutes before you get here) because you don't want them to drug a crazy horse to calm it down. Be wary of people who say their horse has NO problems.
And take your time. Don't rush into this. One thing to consider: If you guys break up, will she be able to afford the horse by herself? I know you think it will never happen, but then, don't we all?
I'm sure someone will be around with a detailed list of ALL the things that you can buy and how much. If you're trying to be minimal and just get the necessities you don't need things like sweat scrapers and polo wraps, but when you own horses these things just kind of accumulate in your possession. We like spoiling our ponies. :p
A good idea: Make a list of things you need, both services and products. Go to your local tack store and get a pricing, and then call the farrier and vet to get a pricing for services (and the price for a farm call). It'll make it easier to see how much you'll have to budget. Good luck :)