It is wonderful that you're learning and starting with lessons! All too often people get a horse first, and then try to figure out how to feed, care and ride, only to find out that the horse either has medical issues, or is way too hot to ever be suitable for beginners, even with the help of trainers.
I don't spend much money on my horse, at least compared to some, and here's what my expenses come out to be: $165/mo for self care board, $66/mo for hay ($5.50/bale*3bales/week), $60/mo for hard feed (a vitamin/mineral, something to mix it in, and salt)= $291/mo minimum, and that does not count shavings, which I get for free and the joint supplement I have him on. Then there is fly spray $20/every 6 weeks and farrier $80/every 6 weeks. And the annual vet visit comes to about $300 for exam, shots and coggins. It's another $200 for teeth. So, adding all that up, we're at $4,852, which actually sounds about right. That's for basic maintenance.
That does not count emergencies, illnesses, lameness, medications, or special shoes that might be necessary. It also doesn't count things that you need but are not things you buy all the time such as your grooming supplies (brushes, combs, hoof picks, shampoo), fly masks, blankets, buckets, feed pans, manure forks, halters and leads. Those things cost me about $1,500 investment when I first bought my horse.
You still don't have tack for a horse at this point, so expect to pony up (at minimum) another $1,000 for a well fitting saddle, girth, bridle, bit, reins, saddle pad/blanket, and any other things you might need (helmet, bell boots, etc).
So, say you get a horse cheap, and that only costs you $1000 (which would be an amazing deal on most sound, sane, beginner-friendly mounts) and you're over $7k your first year of horse ownership. And that is without any "major" unexpected expenses or vet visits, cheap board, and no lessons or training for you and the horse. Not to mention all the extra gas money from driving all over the place looking at horses and getting supplies.
I say this all because you need to know, not because you shouldn't look forward to ownership. I was prepared to buy horse and tack, but when I bought my horse it was all the little 'incidental' expenses that killed me and had me getting a little nervous about my bank account if some accident were to happen. A bucket doesn't cost much, and once you've had a horse for a while you'll somehow have plenty, but when you first get one and have to buy All The Things, it adds up. Make sure to put a bit extra in your horse fund so you're ready for it.