The TPS has a coating which inhibits germination, to remove this you can soak in peroxide or ferment the seeds like you would with tomatos.
You can grow little plants for mini-tubers, you can then assess these mini-tubers for the traits you're after, then grow the mini-tubers on for larger spuds.
Once you're working from seed tubers you are propagating vegetative, cloning, so all traits will remain the same, it's just a question of growing up a few seasons to get full size tubers. As you can imagine a plant grown from a seed the size of a potato is more vigorous, from the word go, than one grown from a seed the size of a tomato seed.