The area your minerals are located in (far NE part of Culberson Co as I map it based on your location info) is a very hot area in the core of industry horizontal drilling for multiple different landing zones.
Cimarex (Denver) is the big player in your immediate area based on info I can access on DrillingInfo.com site. They would be the most logical company to lease to since other companies may not want to lease in the midst of an area that is already mostly held by another company.
Looks like 25% royalty is the norm - getting more than that would be tough. No way to find out lease bonus numbers - that is not on file in public records. But it should be in the thousands of dollars.
Good luck on getting your acreage leased and drilled and getting royalty payments.
Unless you absolutely have to, do not sell your minerals (IMO).
The PDF I have attached shows the purple dots in the middle of Section 34 in your area. Note the widely spaced lateral well bore traces (NS oriented lines). Lots of room for new laterals (can be as close as 500-600' apart in one horizon with multiple horizons having potential)
Hope this helps