Barefoot/Training shoes?

Hi guys!

I follow FB workout programs regularly since beginning of this year. I enjoy HIIT workouts especially. However I feel pain in my ankle after HIIT workouts. So far I always did my workouts with barefoot but I am wondering getting a training shoes is a better idea? I do my workout on carpet + yoga mat. Do you have any shoe suggestion for FB workout programs (since there are various kind of training types HIIT, cardio, strength etc.)

Thanks for all recommendations!