So many options, depends what you like to eat, how much compost you have etc. Your idea is fine, though it is a bit of a myth that "potatoes kill weeds and break up soil" as if they are magic vegetables, most of that is from associated cultivations by the hard working gardener, like earthing up. But anyway with a mulch you don’t need to earth up, and you don’t need to "break up" soil either! I don’t like that phrase. Anyway, potatoes are a good idea.
Winter squash and courgettes are also suitable as you need few holes in the mulch for a lot of growth, likewise winter brassicas such as kale, brussels etc. My books explain this principle, each person can fill in with their favourite veg, and it sounds worthwhile and possible to get the land clean again.