My parents had a similar situation. They live in the country and had invasive buckthorn and weeds everywhere. Many of their neighbors put in sod and dumped chemicals on them, which is terrible for the environment. I'm not sure why people think they need golf course lawns in the middle of the forest, to be honest.
In my parents' case, they let natural ground covers take over the largest portion of the yard. It keeps the weeds down and had a secondary benefit: honey bees seem to love it. Well, maybe not a benefit if you want to run barefoot through there when it's blooming!
For the woodier things, maybe a goat? Haha.
That's a good idea. We have some areas covered in vine plants that seem to control weeds. I jokingly suggested we get goats lol. Cheap lawn maintenance. We'd have to build a tall fence down the hill though. There's a busy road at the bottom of the hill.