I would clean/mow around the trees I would like to leave, put down a
cardboard ring and whatever mulch I had available, preferrably lots of leaves or woodchips, along with some
compost or manure.
Then, depending on how much time you have, and what you want to do there, you can clean more areas, pile mulch there to start improving the soil and plant trees.
However, since I myself don't have much time, and some nicer areas I still need to plant perennials into, I would just leave most of the overgrowing patches, try throwing some desired tree seeds in there, and wouldn't do much there for a couple of years, until trees would start to be visible and around an inch thick. Then I would also start minimally tending to those areas, so I would watch out to keep the desired trees and try to keep them a bit mulched with at least the surrounding sun-stealing vegetation, which I would chop ~once a year and put it around as mulch.
Grazing with animals such as cows and goats would be also a good option to help with clearing brush and grass, and improving the soil of the area, but make sure you well protect the trees that you want to keep.
If you have even more time and resources, you can also scatter clay balls and seed the entire area with soil improving cover crops.