How much would it cost, initially, to buy a horse, and how much would it cost, monthly, after that

That depends on the quality of horse you buy, the quality equipment, if you board it and where or if you keep it at home, if your property is horse-friendly or not, if you have any existing horse equipment (blankets, brushes, stall cleaning materials, etc.). If you plan to keep it at home on a property that is not horse-ready, look to spend probably 20,000 + to make it safe. You will need a barn or run in shelter, appropriate fencing for large paddocks, running water where the horse will be kept, possibly a tractor and manure spreader if you have fields to spread it in, an arena to ride in if you choose... If you did all of this it would likely run you well over $100,000 initial cost, as farm equipment is very expensive.

If you chose to board it or your property is completely ready for a horse, then it would be significantly less. Boarding facilities range from about $175 a month if you're really lucky to over 1,500 a month. Most places tend to be in the 300 range, but also this depends on your location. The Midwest from what I have heard tends to be the least expensive area in the nation from most things, but it varies.

On top of board each month, you will have farrier bills (every 6-8 weeks most likely), possibly vet bills, possibly supplement costs if your horse needs them, and possibly the cost of lessons if you choose to take them. All of this will probably run you around $2-500+/-, but I find that that amount is a good buffer to have per horse. What doesn't get spent can be saved for at least annual vet visits for shots and coggins etc, and possible emergencies.