Given the fact that this has been used as a parking lot. Even just occasionally I would guess without the benefit of checking it out that the soil has become pretty compacted. Most likely to get a big bang for your efforts and expense it will need to be tilled, turned over, disced and then floated level and lightly rolled with a cultipacker. Unless there is a lot of gravel what is there will be worked into the existing soil. It would be worth pulling soil samples from around the property and having it tested. Make sure to “pull” soil 6+" below grade. Amend as the report suggest and then prepare the seed bed as above.
As to seed, depends on what grows best in your area. Given your location you may be limited in selection. In my neck of the woods where cool season grasses grow well, like bluegrass, rye, fescue etc. which are all spreading types verse orchard and timothy which are clump grass that don’t spread out with age. I like to mix 2/3 to 1/3. I avoid adding any clover. It can easily take over a small paddock and it always seems to creep in anyway.
The cost to do the above depends on the equipment on hand. You can rent a rototiller if you have a tractor to run it or rent a tractor with it. But if the soil is very compacted and or there is a lot of gravel I don’t think it will get deep enough for your needs.
If you have crop/tillage farmers in the neighborhood they would have the equipment and usually charge by the acre, $15-30 per acre. But that is for large acreage. For only 2 acres it would depend on how far they have to haul their equipment. For this I would charge by the job. Again without looking at the sight $1000+.
After the seed bed is prepared I would broadcast around 50 lbs of seed, drag and then roll.
So, for the above I would guess around $1,500-$2,000 under ideal conditions. If you have to haul in good top soil that will add CONSIDERBLY to the cost. Plus the cost of fertilizer.
Most likely will want to do this in late August. But that is geographic specific. If things go according to plan you should be able to put horses on it late June, July of next year. Keep in mind that 2 acres is not going to stand up to a lot of horses grazing and or being turned on it regularly. It should stay “green” but not lush green. Don’t turn out when, wet or muddy.
2 acres is basically the size of a lot of rural residential housing. So if no farmers are available or interested a call to a landscape contractor will be needed. They might charge twice as much.
Around here quality 3 board nailed oak fencing is around $5.50 per foot installed.
Installing water lines in your area is a pretty easy DIY because I assume you don’t have to go too deep. You can rent a walk behind trencher. Not hard to operate but not easy either. Bit of a learning curve. Rocky soil changes things a lot. The materials are pretty cheap. 500 feet of ¾" black-poly pipe around here $200, hydrant $50-80, auto waterer depends on the make.
The cost of connecting it to existing plumbing depends on the access to it. 500 feet of direct bury 12-2 electric supply line, $300? Hook up is easy if you know how to do it. An electrician will charge a couple of hundred.