You cant go wrong with bermuda for fast spreading and on a budget. I few plugs or torn pieces of sod will spread pretty quick. Only problem is if it gets proper water it can be maintenance intensive with mowing.

I have seen a lawn done with monkey or mondo grass. Once establish which takes a while it can be mowed/trimmed once a year and left alone. But like I said it takes a very long time to fill in.

You could go all mulch. I big area of wood mulch is attractive and requires virtually no maintenance if applied several inches thick. You could plant perennial shrubs and flowers and have a nice looking landscape that requires no mowing, little water. You would probably need someone to help spread it initially but after that not a whole lot to do.

Except bermuda is fearful if you want anything BUT bermuda (invasive in any flower beds or shrubbery)....it scares me (and I've inherited it at every house I've owned).