In order from tastiest to least:
Purple Dead Nettle:
This weed has a rather minty taste. It has soft fuzzy leaves and can grow quite tall (about 2 ft) if left alone.
Be careful however of the look alike of this plant: in this previous post.
Another commonly seen edible is the wild violet:
Again these plants grow significantly larger if cultivated and kept well watered.
Next is chickweed:
I listed chickweed as third not because of its taste, but more texture. Its a bit stringy. But otherwise its a nice addition to salads.
Fourth on the list is dandelion. Although a bit bitter, the blooms and greens are still tasty in salads.
Lastly is red clover. It is known to be a great herb for health however, it is even more bitter than dandelion. Best to use only the most young and tender parts. Red clover should be easy to differentiate from white clover. A) because it is usually just larger (you can see the white clover in the background of this picture, and B). because it is fuzzy.
These are great weeds to cultivate in whatever green space you maintain. I've been transplanting some into my garden to make sure they are safe to eat since we have a lot of dogs that live in the area. Happy Spring!