This is a great topic. As already mentioned, it is amazing how clover, dandelion, and plantain are sort of a natural vegetation for lawn-like areas. I encourage them and get them for free.
A plant community could also include grasses. I have had good results from low-height fescues, which are deep rooted, tolerate moderate shade and tree
roots, keep an armor coating on the ground year round (even when dormant), and are vigorous but not aggressive, so as to fill in nicely between the other plants. These are cool season grasses and become active fairly early in the spring when rains are heavy to aid in
water management.
In general grasses grow well with clovers and take advantage of the nitrogen, and fescues don't require any additional inputs due to the deep
root system.
Ideally the plant community would have both warm and cool season varieties of broadleaf and grass. For warm a season grass, I been considering adding buffalo grass to the mix.