There is little controversy among advanced freestyle players with respect to shoes. Almost every player agrees that, at present, the best-suited shoe for freestyle footbag is the adidas ® Rod Laver nylon-mesh tennis shoe. The reason it's so good is that the sole is thick and good for absorbing shock, the inside surface (for inside delays, clipper delays, etc.) is flat, and the shoe has an "open toe" design, making a nice flat area with no obstructions for stalling the footbag on your toe (after you modify them -- see the next question in the FAQ you're reading).
This recommendation is valid for every level of player; even the first-timer will find this shoe remarkable for playing footbag, especially after they are modified and laced properly.