Hi Mary -- welcome to garden.org !
The long shoots result from the potatoes being in the dark; when you see sprouts beginning it's best to put them in an area where they get light during the daytime (not direct sunlight, just in an area that has fairly bright light and preferably is rather cool). It seems a little counter-intuitive (at least it does to me), but the sprouts will grow very slowly in those conditions. But yes, I would go ahead and plant the ones you have, as carefully as possible. Some might break off in the process, but I think they will grow just fine for you
