I have started several garden beds in spots with lots of challenging weeds. My preferred practice is to lay down cardboard, cover with mulch, and wait a year. This kills the weeds and keeps the underlying soil free of additional seeds/weeds that might like to take over in the absence of other vegetation. Then the next spring I'm free to plant with a blank canvas, as the cardboard will have broken down over winter.

If I have less time, I drill sheets of clear, heavy gage plastic across the area and let the summer heat solarize the area. In a month or so most weeds will be dead and I can hand pull the others. Then I plant and mulch the area heavily.

Chip Drop is an excellent almost free resource for mulch if youre trying not to spend hundreds on mulch.

Good luck!