Much will depend if your parents are on board for this. Are they horse people? Will they mind the money that horses require for their board/vet care/ farrier care?
The breakdown of what a horse costs varies. You didn't say if you know what average cost is for keeping one horse a month, but I can tell you what it costs for me, and you can add the amount it would cost to board at the stable you are familiar with.
I have 3 horses, and I get a break on my newest horse's board, so for all 3 I am now paying 250 a month for pasture board, (100 a month for each of my two older geldings, and 50 for the 3rd one.)
I pay the renters in the house on property 30 a month towards their water bill, *which I know the one horse that has to be kept on dry lot more or less is not drinking that much but still*.
I have to grain and hay him, I pay 3.75 a bale for square bales of good grass hay, which is stored at hay growers house, so I have to haul it 20 bales or so at time. I paid 4 for some slightly better grass hay that is at the barn where horses are.
Trims for the 3 horses, is 50 for the older ones, and 35 for the younger horse. He will have front shoes on soon I imagine, so that will be 100 dollars, that expense repeats every 6 weeks or so.
Worming, vaccinating I do myself 30 dollars for the vacs yearly, give or take, 60 or so yearly for wormers. That is per horse. Supplements are more on top of that.
Grain is 22 a hundredweight right now, and go through a bag a week per horse, so 35 dollars a week.
Minimum you can expect to spend for boarding a horse in city is 300??? And can't see that would include feed/hay and for sure not worming or vaccinations or farrier? And if you want turn out, or blanketing, some barns will do that in board bill, but others charge for it. And you have to buy your own blankets too.
Minimum I can see this costing is 500 a month, factoring in vaccinations/worming and farrier. And could cost more very easily. And didn't even figure on dental either?
Horses are expensive to keep if you do it even halfway right.
You might be better off looking at trading barn chores for a partial lease on a horse already there, that someone else is responsible for financially.
Horses make me a better person.