I have been mowing brush and high weeds all summer. I started out with a commercial grade weed eater, then a DR trimmer/mower (string) powered by armstrong. I rented a Billy Goat by Outback, then I bought an older DR brush mower with one wheel drive. I rented a tractor with a brush hog (that made me real lazy). For your size piece of property my recommendation is, 1st tackle it with a weed eater, it will take most of a day but you will uncover the rocks and any stumps or other obstacles without killing any expensive equipment. If you have saplings or small trees a homeowner grade chain saw will take care of them. Be sure to remove all wood over 2 inches in diameter if you plan to use a walk behind mower. Once it is knocked down you will be able to assess how difficult it will be to to keep it that way. If it is real rough or over 20 degrees slope, the weed eater will be your best option. Slopes up to 45 degrees can be mowed by working up and down only, no side hill travel because the machine will tip over and roll down the hill. Without seeing your land it is hard to say which machine may work best for you. If you don't have a lot of rocks and can work around them a rotary or cicle bar mower will do very well and cost a lot less than a flail. A flail or a string machine are your only options if you have a lot of rocks or stumps and want to get done quickly. I frequently use the DR brush mower and then clean up around the obstacles with a weed eater.
The reason I mentioned the Orec is the dual hydrostatic drive. There is a rotary machine with dual hydrostatic drive. It is made under the Stanley brand and is also marketed by Home Depot with a larger engine. It is called The Beast. Dual hydrostatic drive allows you to control the speed of each wheel separately. On rough ground that will save you huge amounts of effort trying to keep the machine on a straignt path. Bumps and holes cause the drive wheels to turn a two wheeled machine off course. With dual drive the machine's power corrects the course instead of you having to muscle it back where you want it.
My DR only drives the left wheel, it is a real workout to mow even a half acre of flat ground. I recently put in seven real hard hours on a half acre of tall grass and thistles working around stumps from an old tree farm using the DR. The newer DR machines are better, with wider tires, articulating mower decks, more power and differential drive axles with optional locking of the differential for better tracking.
Another machine to consider if you have other machinery needs is a walk behind tractor. These two wheel tractors are available from many manufacturers and there are a wide variety of attachments available for mowing, tilling, hauling, snow removal, etc.