Looking for a yard/woods grass that fits these criteria:

[rgG]

If you don't do the prep, removing the debris, IMHO, you are just throwing your money away.
Sorry to be a Debbie Downer, but good prep is at least 75%, probably higher, what you need to ensure that anything you plant grows and does well.
If you don't do anything, it will weed up on its own and cover as well as anything.
I know you want it to look better now, but unless you can get it cleared, you should just leave it as is and let nature take its course.