I don't know if anyone else said this, but a horse shouldn't be kept alone, and one acre isn't enough for two horses.
Sunny, I noticed that too, and I agree completely. Horses either get mad or depressed when they are on their own. Most people who think their horses are OK alone have the depressed variety. It is their most basic need, more than sex, more than food, they need companions. Horse training uses this need - think about Monty's join-up, Parelli's games, they all work by isolating the horse from his herd and then putting the trainer in its place. Horses, who do not regard us as predators as we have never in history actually sunk our teeth into them while they are alive, will accept us as protectors and guides in the absence of a stallion or alpha mare.
However, back to the question! You need a companion and you have limited space. But it is quite possible if you plan and arrange properly. The fact that you even posted the question shows that you are thinking ahead.
Do not be tempted to get a mini as a companion - they are major escape artists and the management of two equines with wildly different nutritional requirements is very complex and time consuming. Do not be tempted to get a rescue as a companion either, they are likely to require more care and involve more expense than your main horse. Instead, why not see if there is someone local who would also like to keep a horse simply, and would board with you.That way you could share yard duties - one of the worst on a small area is picking up the dung every day, you have to, and it is about a barrow a horse.
What you need to do with your acre is divide it into three parts. About a quarter needs to be a barn with a dry standing as we call it in the UK - that means a yard with a surface that doesn't churn to mud in the bad weather. I use road planings for the top surface - I don't know what they are called in the US, but it is the top surface of roads that is scraped off when a road is repaired. The remainder needs to be divided into two, to allow the horses some pasture turn out. You only turn them onto it for about 3 to 4 hours a day, the rest of the time they are yarded, so you will need hay or straw for them to nibble all year round. In the UK, the grass cycle is about 3 weeks, so you turn them onto one bit for 3 weeks, then let it recover and grow while they are on the other part. It is hard work keeping horses on a small area, but to keep them just at grass you do need 2 to 3 acres per horse, depending on the quality of the grass.
When you buy your horse (I too think a lease to start with is a good idea) remember that you will be spending $100s each month to keep it, so it is worth waiting a month or two and buying the best you can afford. By that, I mean, sound, good mannered and an easy keeper. These horses fetch a premium price. Spend the money on having leg and foot X-rays, have ultrasound to look for ligament damage, check everything as if it was a $100,000 horse, because once you own it, you will love it, and if it is unsound you will find all your money and some is spent on vets and special care, and you don't get to ride.
Post a video of the horse in action here for critique, I expect many people on this forum can spot unsoundness from a video and BTW, walk without a rider in a straight line is the best gait to show any unsoundness. Go for a horse that is about 8, proven, but young enough to resell if your life changes. Also, but this is a personal thing, I avoid like the plague anything that was backed before it was past its third birthday. They are the ones that get bad backs and develop arthritis young.
I can't really comment on actual costs as the UK is so different, but we keep 9, on our own land, and the feed etc still costs over £1000 per horse per year. We spend that much again on the land, but we are in a long term building programme.