New Home, lots of work to do

Just bought my first home in Fort Worth, TX and the backyard is in rough shape. Lots of weeds. There is no irrigation system, so I have been using a hose-attached oscillating sprinkler to keep the cracks in the soil at bay… what’s the best way to improve here?

If to start from scratch, has anybody had success with putting down tarps for a few weeks to kill everything? I’d rather not use herbicides at scale if I don’t have to. Thanks in advance for the help