Shoes for HIIT?


I've been doing Fitness Blender for a couple years now, and except for the PFTs, I've always worked out barefoot. However, I've heard that it's not great to do high impact in bare feet and I'm really unhappy with the shoes I have for doing the PFT, so I'm thinking I'll get some shoes. The question is: what am I looking for in shoes? There's lots of shoes for specific sports, but other than the PFT, I'm not a runner, so I'm not exactly sure what I'm looking for.