Half an acre, covered in other stuff? No, I don't think that warrants a ride-on, but a large, good quality motor mower to walk behind would be fine. It would be easier to cut around the trees too. On a ride-on, once the trees get big with overhanging branches, it's easier to duck under them with a walk behind, than get your face smacked and your hat swiped off by branches on a ride on. You have a smaller turning circle too.
However, if you are older or unfit, or either of you would get to hate doing the grass if it took time and was hard going, then maybe a small ride on would be ok, but for rough ground you would really need a big toughy, which would cost and not be manoeverable, so back to square one. If you're rich and can afford two machines, then an Allen scythe would do the rougher bits - I think you can hire them in fact, which would work better as you would probably only need to use it occasionally.