Backyard challenges - need help
I'm a first time homeowner and just got our house last fall. There are some challenges with our yard, especially the backyard. The backyard sits up on a hill with a ditch around it that I've dubbed the "moat". Due to the ditch, the 6' fence sits below the main part of the yard, so you can easily see over it when sitting on the patio.
The ditch is a disaster that we've started fixing up at least on the one side. It's riddled with weeds and trees that spread (locust, etc.). I put in 4 veg beds and put down mulch, but the weeds keep coming. On the other side of the moat is still terrible. Lots more little trees/bushes, weeds, and lava rock. I guess the previous owner thought that might help suppress the weeds, but it just makes it even more of a pain to do anything. Would I have to remove all the lava rock first before doing any beautification?
On the north side the moat continues, but there are 3 large bush things that are swamping the whole area. However they don't grow large enough to block the neighbor, and they look all spindly and terrible in the winter.
I don't know where to start. Any advice would be appreciated. I'm also not sure if everything in the moat is a weed and should be ripped out, or if some of the plants should be left alone.
The last part of the pics is of this giant bush/ground cover that is half dead in our front/side yard. Is there any way to salvage it, or are we going to have to tear the entire thing out?