I think any kind of running or cross training shoe would be fine. The key is to keep your toes in the holder and not lift your feet. This was one of the things I kept having to tell myself when I first got my Nordic Track years ago. The natural tendency is to lift your feet but the Nordic Track requires that you slide them back and forth.
Good luck and keep at it. Once you get the motion down, it'll be second nature.
BTW, I've never been in better shape since I've been on the Nordic Track regularly. I hope you have the same great results!