If you spray Roundup it will kill the weeds & the grass will come back; if it's mostly weeds then what do you have to lose. Pulling weeds after the ground has been moistened is the easiest, like after a rain.

As far as the removal of unwanted items, last resort should be a landfill directly, they usually charge a straight fee; I use the Bestway Transfer Station off Marksheffel & Space Village, they charge by weight.

I recycle as much Wood, Rock, clippings, metal, etc. etc. as possible; it's usually cheaper than the dump.

Try to re-purpose as much as possible by redesigning the layout & incorporate the desirable pieces you already have on hand .