If you don't have time for daily milking, I'd say beef cattle might be the best bet. I'm pretty sure fencing off 3-4 acres with goat-proof fencing would be way out of just about anybody's budget. Cattle fencing is much cheaper (but 3-4 acres of it is still going to be many hundreds of dollars). It does depend on what sort of plants you've got growing in the pasture- you'd want to be sure it's good enough to keep cattle (or whatever animal you decide on) thriving on.
We have sheep, too and they do keep the grass mowed totally down in the areas we put them. We put them away in a barn every night so haven't lost one yet to predators (we're also right next to a forest full of predators). The sheep are WAY easy to care for, but the require much better fencing than cows ( =more expensive), but not as extreme fencing as goats. We raise Katahdins which are hair sheep so I don't have to bother shearing them every year.
If you raised beef cattle you could sell the babies, or sell the meat depending on your state's laws, or just enjoy your own amazing grass fed beef for yourself. :)
Don't forget you'll have to feed whatever animal you decide on hay all winter or whenever your grasses die down.