you might look into letting someone use it for hay. I have 2 or three places near my ranch that let me cut hay to supplement my winter supply. not only do I not charge for this, but- if they were not family friends- they would likely be charging me for the hay.
I agree with most of the above, especially Lorinada’s suggestion to only regularly mow only a small portion, except I’d point out that in many areas “letting it go wild” may be an invitation to colonization by undesirable invasive plants rather than the native species that are most desirable from a conservation/wildlife management standpoint.
As others have mentioned, there really is no solution in your price range to keep the entire property mowed at lawn height. If you want to keep the land as meadow, you’re stuck Bush Hogging once a year at the minimum to keep shrubs out. There’s no way to purchase this equipment on your budget, so you’ll have to pay to have it done. If possible, wait until after ground nesting birds have fledged.
Without knowing where the property is, I can’t speak to the best management strategy, but I guarantee someone at your local University Extension Sevice or Conservation District can, and they will be more than willing to help you out. There are a number of conservation programs offered to homeowners through various agencies and organizations- at the very least you can get lots of information about managing your land for wildlife and native plants, and you may even find you are eligible for various grants, tax breaks, conservation programs, easements, etc. if you are willing to maintain the land within certain guidelines.
If you are in a rural area, you may find there are all kinds of barter opportunities. Others have pointed out the possibility of letting grazing animals use the property , but without fencing this is not so hot an idea. On the other hand, maybe your neighbor with a tractor and Bush Hog mows it once a year for the priveledge of dove/deer/etc. hunting. I noticed from your profile you are a teacher. Perhaps offer tutoring services in exchange for bush hogging
Or you can do what I and most of my friends do, which is to disable the safety interlock thing, or else use a cable clamp to secure the handle in “run” mode.
My advice for the OP would be to look into alternatives to grass for the majority of the 3 acres. There is a forum devoted to alternatives to mowed grass:
http://forums.gardenweb.com/forums/
vetbridge and anyone else who’d know: the site about lawn replacement recommended aguja chocolate chip, which never needs mowing. Is this a good idea or a terrible one? Do I have to somehow get rid of the grass that’s there now in order to convert it over? Will it screw up the ecology of my land in a way that’ll make me sorry I did it? Also, how much seed would I need?
I really need my ignorance fought on this one.
Sorry, that was “Ajuga chocolate chip.”
http://www.stepables.com/store/Scripts/prodView.asp?idproduct=18
It’s $288 for 72 plants. I wonder how many I’d need for my whole lawn…wish I’d payed more attention in math class.
I think they’re saying to space them 8" apart. So figure eache plant will cover an 8" by 8" area, or 64 square inches/0.44 square feet.
There are 43,560 square feet in an acre, so figure you’d need 99,000 plants per acre, or about $396,000 per acre. That’s not counting any seed bed preperation/grading/drainage work that may need to be done, although that’ll be an itty bitty figure compared to the cost of the plants.
There’s a reason bush hogs are more common then “Ajuga chocolate chip” in rural areas. 
Ajuga is a great groundcover. It spreads over time. I have used it after rototilling an area. I would not space them as closely as the garden centers might advise (they are in the business of selling plants).
For your area there may be other suitable ground covers that may be cheaper. Some groundcovers are considered “weeds” and are very invasive (which makes them ideal for your situation)…
I don’t know where exactly “South of heaven” is, but I second talking to your local Ag extension or county ag dept. I’ve got about 5 acres of lawn and next year a large portion of that is going to be seeded with native prairie grasses and wildflowers at no charge thanks to our county land office.