Disclaimer: I dislike grass farming, and dislike the suburban pressure surrounding it.
That said, recalling my previous attempts at caring more:
- the best way to keep weeds at bay is to have healthy grass
- the best way to have healthy grass is to have healthy soil
- most suburban neighborhoods are formed by scraping all the healthy soil away before building the house
- leaving you stuck with fake farming methods like petrochemical fertilizers (Miracle Gro) and lots of water
- and killing weeds actively, rather than by choking them out with the Suburban Dream (healthy grass)
So it's an uphill battle to begin with. :(
When I sold a previous house, I just paid $300 the fall before the house went on the market to aerate, seed, weed-kill, and fertilize. It was one or two treatments, and I think he was selling a loss-leader to entice a subscription care service. You might look for that.
You can also do a ton of research and overhaul your lawn yourself. You might have friends with core aerators (the only useful kind), or you can walk around with
one of these.
Weed killing is funny, since you want to kill everything but the grass. If you have no grass, then, well, that's a different problem. It boils down to:
1. Killing broad leaf weeds with something like 2,4-d
2. Spraying a pre-emergent herbicide (inhibits germination) in early spring to prevent crabgrass
Since you have more money than time, and since you're considering selling it, you might try the lawn service as an investment in the sale. Probably worth more in value than anything you spend inside the house. With those short-term fertilizers they should be able to get enough green out of your grass to make it pretty and sellable. Expect to mow and water, though. :P