When it comes to working out in Kung Fu, your footing comes first. This should be obvious, since grounding and balance comprise the foundation of your stance and movement. But some practitioners don't really consider their footwear.
Wearing rigid, thick-soled running shoes may look good and work very well for actually running around a park, but usually they're not great for working out in a martial arts academy. You need to be able to pivot smoothly and quickly on interior flooring to accomplish the demanding, precise transitions Kung Fu requires.
Hence the continuous, long-term popularity of the good old cotton-soled, canvas Kung Fu shoes, the cheapest footwear you can buy other than thongs. Supple and light, they have a flat, thin sole with shallow traction ridges that allow smooth movement. Inside, the white cotton lining and inner sole provide long wear and comfort. Outside, the practical elastic inserts on each side of the top of the shoe adjusts to almost any size foot.
Traditional women's canvas Kung Fu shoes have no elastic inserts on top, but a strap and buckle to keep them on. Often you can find them with pretty embroidered designs on them, like dragons or flowers.
These shoes are great for Tai Chi too, outside on grass, tile or even dirt surfaces. On an extremely glassy floor, or just-waxed surface, the wearer should be careful; since they're meant for quick movement, they will slide if you don't transfer your weight just right.
The key to getting used to your chosen footwear is the same as with the rest of your Kung Fu: practice, practice, practice. If you fall, you've learned something. If you don't... you learned something, too.