I think you are right in taking a soil sample first. Another idea would be to dig some holes in vaious locations to check out the depth of the soil. The deeper the soil, the more nutrients and water the soil can hold, the better plants will grow. I would guess there are areas around the fields where you can see there is thicker and taller growth. These would be the first place to check out, and probably the best places to put in a food plot.
Wait until you get the soil test back before you plant perennials (alfalfa/clover). You may need to add lime to the soil for them to be successful long term.
Winter rye can be planted in August, will tolerate poor soil, is a great green manure crop, deer love it, and its cheap! Winter rye would be a great choice if you want to plant something this fall for the deer and for green manure.
Since you are rather new to food plots, I would suggest you wait until the spring for anything other than winter rye. You can use the time to plan where you will plant, what you will need to get, and where you will get it. Do some research and ask some questions, and you will be happier with you food plots (for example, have you thought about weed control?).
There are a lot of great places to buy individual seeds online, or at a local ag retailer (co-op). They can also help you with variety suggestions for your local area. In general, the seed mixes you see on TV are not worth the extra cash.
Good luck with your project. I am sure you can be successful with some research and work.