Last fall we bought a home with a very neglected lawn in Denver. We are new to this arid mountain area. The lawn is full of weeds (short plants like a ground cover, broadleaves, dandelions, etc), a lot of bare spots & a little bit of grass (type unknown but stores are selling Kentucky mix). Some crab grass. The soil is very compacted clay, slightly alkaline. Sprinkler system not functioning. Water ration: 2x week. Where do we start?

Have thought of aeration/lawn racking, followed by preemergent (what kind?). Then amend with clay buster product --do they work (which one?) or gypsum & aged manure? Don't have any worms. Should we till or not since there are lots of weed seeds?

How long after preemergent can we plant seed? Are plugs better? Can't afford sod. When do we fertilize? We need to establish deep roots to survive the arid climate.

A few shrubs are starting to bud. Forsythia should bloom very soon. We are also tearing out overgrown shrubs. Do we have to dig out all the roots? Will be planting roses, hydrangea, peonies, lilies, iris & tough shrubs.

Would very much appreciate advice about specific order of care and brands. Never gardened in this climate before! 65 deg today & tomorrow going down to 9 deg & a ft of snow!
Many, many thanks.