Since you are on the John Deere forum, I am assuming John Deere is one brand which you are considering. My inlaws have some property in Nelson Co. VA, so I am familiar with the terrain in and around Roanoke. I will say there likely is some property you have that no tractor could operate safely, but in the JD line, the 4000 series is going to be your best option. I am familiar with other brands, but not to the degree as JD. I know Kubota has some low COG machines that in are that HP range as does New Holland. My feeling is in the JD line, you may wish to consider looking for a used 4010 series (the prior series to the current 20 series) to stay in your price range. They are rare, and have Yanmar powerplants which are well-proven. They also are often leased by hospitals, etc., and may be available that way. I do not know about the dealers in your area except to say that there is a James River dealer in Stuarts Draft just off 81N (I do not know them) that is a larger dealer. They may have some insight into the current availability of a 4010 machine in your desired HP range. Though I think it could do your work, the 3000 series (mid-frame) compacts from JD at least are not as stable on hills as the 4000 series (or old 4010 machines) due to their shorter wheelbase and higher COG. Trust me, having had both and living where it is hilly, I know this. You could surf MachineFinder as well to look/compare these machines and prices or you could take a chance with Craigslist, etc. For less than $20K, you likely are not going to find a tractor in this size range that is new, so lightly used may be your option, at least in John Deere.
John M