Yeah, I agree. If you are looking for the least effort way to do it, pay someone else. Let them handle the equipment maintenance and repairs and do the sweating. It will cost you less money in the long run and give you more free time.
If you cannot find someone to hire, for whatever reason, then get the biggest pull behind rough cutter you can afford and an ATV that can pull it. Most small tractors pull a 5' wide mower, so if you can find something between 4-6' you will be in the same production range as a tractor/brush hog combo and the cutter will only run you a couple thousand new. If you know a good mechanic that can check things out, you might save a few bucks buying used, but the maintenance will likely be higher.
Depending on how "rough" you want it to be, you can get by with a few mowings per year so your investment in time and equipment could be kept fairly low. I expect it will take a good portion of a full day to mow 10 acres even with a wide cutter and a fast ground speed.