I would recommend the low growing Dutch clover, it is what I use just about everywhere. The buckwheat will die off if you chop it as it is turning brown at the end of the growth cycle. Peas and Beans will also die if you let the plant go to maturity before chopping or if you cut it off right at ground level in my own
experience.
I personally do not like vetch as it is a
perennial and would need to be dug or pulled up roots and all. I don't like morning glory for the same reason of nearly impossible to get rid of it once it is established.
My personal choices of cover crops were made as a result of what we grow and how we grow it. I use Crimson, Dutch clovers, Buckwheat, Purslane, Austrian peas and annual yellow sweet clover.
All these get mowed down just prior to planting our crop plants (transplants). By the time any of the covers begin to make their comeback, the crops are already established and not taken over by the covers.
The buckwheat and peas have never made a comeback on our gardens since we cut at 1/2" above the ground or lower. The clovers do comeback but it takes them around three weeks and they never hurt the crop plants.