We have your problem--about 2 acres of lawn, brush and weedy pasture, one push lawn mower, one weed whacker with attachments (12" cultivator). For the last three years we've rented a walk behind brush hog to clear blackberry bushes and heavy brush. We rent a heavy duty walk behind tiller to prepare the garden, and we use the small cultivator to keep weeds down. The weed whacker with attachments has been very handy. We have a service contract on it and the lawn mower, and we get our money's worth out of it. We get them tuned in spring, and they get a lot of hard use.
I realized we wouldn't be able to have a big garden and keep ahead of the weeds in the old pasture, so I started lasagna gardening. The soil is clay and really hard packed (it was overgrazed by horses). Putting cardboard on top of the soil and layering it with straw, leaves, stall manure and dirt makes good beds. You can start the beds in the fall and plant in the spring. The cardboard suppresses the weeds and encourages worms to break up the soil. Eventually the cardboard disintegrates, and you're left with a deep bed full of humus. No power tools involved, just your own labor. So far I have finished 1 bed for blueberries, and I am working on a second.
I have a friend who did her very large garden this way--she spent a year collecting cardboard and gathering free materials to go on top. She has poultry that provide the manure. She composted all of her kitchen garbage in the garden. She got leaves from neighbors and talked people into giving her free rotten straw bales. Now she has a very fertile garden with great tilth. She adds more mulch every year.
My city utility board offers free "chips", which are shredded and chips tree limbs and trimmings from the power line crew. You just call them, they deliver 4 yards of material to your place. I am going to get all the chips I can and put them on top of the cardboard. I'll buy more horse manure--I found a source for $4 a small truckload. I'll also mix in some alfalfa pellets to heat up the pile. I'll sheet compost this, cover it up with a piece of plastic and let it cook down until next spring.
Although I think with a lot of work we could transform the entire pasture, I still want to buy an old 1950's era tractor a friend of mine is selling. It can do so many things around the place: mowing, brush hogging, cultivating. Our local implement store will rent post hole augers and whatnot. The price of the tractor is half that of a decent heavy rider mower.