Weightlifting Shoes
* Choose shoes with a flat bottom and hard surface.
* Avoid running shoes with a soft bottom.
* Shoes specifically designed for weight-lifting have an elevated heel designed to help you balance.
General Gym Shoes
* Stick to shoes that provide you with ankle support.
* Look for cross-trainers or running shoes that provide some cushion.
* Choose shoes light enough not to make your feet feel heavy.
Running Shoes
* Choose shoes with enough cushion to absorb the running impact.
* Make sure they support your ankle
General Shoe Tips
* Leave about half an inch from the end of your big toe to the end of the shoe.
* Replace your shoes after 300-400 miles of usage.
* Make sure they feel comfortable at the store before buying them.
References
https://www.health.com/fitness/how-to-find-the-right-gym-shoe
https://www.webmd.com/fitness-exercise/features/how-choose-athletic-shoes#2