Just bought a place and trying to get my backyard into decent shape. Right now it’s kind of a mess with a mix of patchy grass, clover, random flowering weeds, and a bunch of bare spots.

Any suggestions on the best way to get rid of the weeds without nuking the whole yard (trying to avoid heavy herbicides)

The soil is pretty compact/clay-heavy in spots. Should I be aerating or mixing in compost first?

Also considering turning the area around my AC unit into a small raised bed (maybe mulch + shrubs or something low maintenance) since that section is already rough and uneven anyway.
Goal is something fairly low maintenance, not perfect golf-course grass, but want it to look clean and fill in nicely.

Any advice, ideas, or things you wish you did differently would be awesome.