Great advice so far. Especially on the soil sample. You should be doing that asap and amending the soil so it's ready to plant when you are.
I would definitely be looking at putting in a water source in your case. It need not be next to the plot but near by. In fact I'd put in a location that deer have to move to and place it with stand locations in mind. Ruminants need a lot of water. Bucks drink a lot of water during the rut, especially if it's warm. Something as simple as a plastic swimming pool buried in ground that you fill can make a difference. Lay a stick in for critters to climb out if they fall in.
Trying to offer some thoughts on your other questions. You can make it as big or as small as you want. It's not all about size. Deer densities can affect plot size but unless you have access to farming equipment to plant acres, which you don't have, of food you won't be able to keep up to browse pressure anyway with a decent deer density.
You can let the deer tell you what they prefer by planting 2 or 3 different options either in strips or as a mix. Monoculture plots are typically not a good idea. Should you get disease or pests they can wipe out the entire plot, and deplete the soils of specific nutrients.
You mention farming in the area, most likely corn, beans, alfalfa?? You can plant things like brassicas in the mix. Deer typically browse these after a frost, when the starches turn to suger, so ag crops may be less available. You aren't necessarily competing with the ag crops directly, so to speak, just offering something different. It doesn't sound like your equipped to plant corn and beans anyway, and not on that small of a plot. Deer don't graze, they move between food sources regularly so offering different options is not a bad idea.
Irregular shaped plots have some advantages. They offer security and ambush points for stand locations and can also keep unwanted shiners and passersby by from seeing into your plots, and the deer in them. If you want to be able to hunt the entire plot, for example using a rifle form greater distance, then shape it accordingly.
You bring up "plowing". I wouldn't recommend that. Plenty of plotters do just fine with a little gly, some seed and timely rains. There are better options than plowing and unleashing the seed bank.
My perspective comes from providing year round food sources for wildlife, improving the habitat and health of the soil. If your just looking to put something in to harvest a deer over, and there is nothing wrong with that as far as I'm concerned, then pretty much anything that stays green late into the season will do.
I could go on but this is getting long winded already.
Good luck. It's addicting and as much fun as the actual hunt.