When purchasing the best shoes for elliptical, you generally have to choose between cross-trainers and running shoes. Both provide you with the appropriate support and stability when you are exercising with your machine.
With that being said, there is a difference between the two. Running shoes help you move forward. They are light, flexible, and are usually used on flat terrains or surfaces.
As for cross-trainers, they have wider platforms that help keep your feet and ankle stable. They are perfect for low-impact elliptical. The choice of either one will depend on your preferences.