I would not turn it all into a hay field if you want to have good hunting as you said in your own words. Deer spend much more time in cover during daylight than they do in hay fields, just a thought. In my experience, overgrown pastures serve as great bedding and would be best to let continue as such, however I would mow some spots down to turn into hunting plots based on prevailing winds and best stand locations for them, consider your entry and exit routes too, 14 acres is not big, but if you are careful not to spook them coming and going it will hold a few deer.
I also like mowed paths thru such cover a lot for influencing deer movement past you stands, you can improve an existing trail this way, and also create deer movement from bed to feed as well. Given the choice the deer will walk a mowed path more times than not, past your stands perhaps, on the way to feed or bedding.
Just consider your end game carefully, do you want hunting, or a field full of deer you need a spot light to watch? If you maintain it as 14 acres full of food, the majority of the time the deer will be bedding on someone else's property during shooting hours.
Good stuff. I'd consider planting some evergreens as a visual barrier with the neighbors property on the west side.
Most of the rest of the land you could manage as "old field succession", letting it grow up, but controlling things, mostly with a brush hog.
Warm season grasses do make nice cover, but establishing them can be tricky, and there is a fair bit of time and expense required.
If you let a hay field like that go for a few seasons, you will probably get a mix of grasses and goldenrod and other forbs.
The goldenrod grows tall and thick and can provide cover much like the warm season grasses. And it usually comes in on its own. No need to till and plant etc.
You will also probably have invasive shrubs such as autumn olive and multi-flora rose, which are very common. And maybe also honeysuckle, and barberry. My advice is to control these invasive shrubs, with the brush hog and/or weed wacker with a brush cutting head, loppers, herbicides...whatever weapons you got. Don't let them take over your land. And if you get tree of heaven (ailanthus) kill them. Don't tolerate even one on your land.
You may also get native trees coming in. Walnuts often come in. Sometimes locusts. Sometimes white pines and oaks. Depending on what's in the neighboring woods.
You'll have to decide how many trees you want or don't want. When they are small, you can just brush hog them down.
Much of the management can be done with a brush hog, to decide how low and grassy you want various spots, or how tall and thick. A patchwork is good.
You want thick areas for cover, but more recently cut areas will be good for shooting lanes, and lanes for both you and the deer to walk, and will have forbs and maybe clover that deer love to eat.
Starting out, think about where your stands will be and your shooting lanes. You don't want to shoot towards the house and road.
Then think about where the cover will be. If there is cover, the deer will stay there during the day. They will bed down in tall thick goldenrod.
As others have said, if it's all open, just short grasses and food plots, the deer will feed there at night, then go somewhere else to find cover during the day.
Liming might be a good idea, but do a soil test first. Penn State only charges about $9 for a soil test. If it's a fertile soil you may not need to add lime.