rdln is correct that your best bet is to check the USGA site for proper construction. Lots of sand for proper drainage is a key. Our course is mowed daily and a hand reel mower will work just fine for yours. I don't know the kind of grass you will want back there in Virginia, maybe Bent? Checking with local nearby courses will give you insight as to what is needed in your specific location, as there are mini-environments in every area that affect growth and maintenance specific to your green. Even on our course, each green is treated almost separately since some are in shade and others in the sun or some at higher or lower elevations. Try to get yours in the sun, away from shade to give it the best chance.
That said, there are many golf courses (like ours) that have old "push-up" greens are doing fine. We do aerate them 2 times per year though. They had no special preparation and were just maintained well by the old superintendent who knew how to "grow grass". After 85 years we have rebuilt only 3 of them, and the new USGA method is incredible with its preparation (and costly).
That sounds like a fun project and you should have fun on it. Putting (and chipping) practice will surely lower your scores. One suggestion is to be sure to have at least on section of it that is nice and flat. It is tempting to make it all sloping with lots of break and mounds for fun, but you will want one section where you can practice seriously. Hitting the put in the direction you think you are aimed is a key to great putting and a straight put will show you that.
Keep us informed of what you are doing there.... and shoot low.
Thanks,
