The type of weed flourishing in a particular field is often an indication of what the field has an excess of or what it is in need of, so it might be worth doing some research on dandelions.
I tend to leave things to try and balance themselves naturally, though of course with some human intervention. My first fields were completely overgrown with thistles and docks to such an extent I could never even see let alone find my Jersey cow!!
I topped when I could and took hay crops, spread calcified seaweed (used to be available in those days, in fact it was so rarely used it was difficult to come by and expensive) Mixed grazed it with sheep and cattle and it is lovely mixed meadow now. Probably too many buttercups, and I am sure I could easily increase the fertility by a bit of muck, but I like the old wildflower meadow look
never sprayed it, seeded it artificially fertilized it and I have sorrel, wild white clover, large red clover, many variety of grass, nettles round the edges, still some thistles and docks when it is not topped regularly or not grazed hard enough. Plus loads of butterflies, moths, grasshoppers, grass snakes, newts, frogs toads, and masses more including bats, and seven nests of swallows that regularly produce at least 2 to 3 broods per year.
My take is that steak and chips is very nutritious and filling but I wouldn't want to eat that every day for the rest of my life. So rye grasses might be the most productive, but may not give you the healthiest animals, and certainly wont give a varied fauna, never mind outcompeting the flora
But it depends on which direction you are looking to go, and commercial farming needs to be done to feed the world to the standards we require, so I am not saying my way would be for everyone.
All the best,
Sue