Y'all know I'm a big fan of training barefoot or with socks only, but I also understand that not everyone feels comfortable with their dogs out while lifting. Plus, for those of you who go into a gym facility that is not in your home, I highly recommend wearing shoes to protect your feet from whatever is on the gym floors. I did a science project in middle school testing the bacteria in the locker rooms and I will never go barefoot in those places.
If barefoot training isn't an option for you, I highly recommend getting a shoe that provides a wide toe box (this is different than just a wide shoe) and flat bottom. A wide toe box allows your toes to spread out as they are meant to to create a stable base. It's hard to stay stable in your footings if your toes are jammed together, right? Right. Having a flat bottom to the shoe is also encourages stability.
It's common to see many people wearing running or walking shoes at the gym, but just because someone does something doesn't mean you should do it, too :). Shoes like running shoes have a harder time stabilizing for a couple reasons. 1, the shape of running shoes bring your toes up to help with walking/running strides. 2, because the toes are pointed up, you can't plant your whole foot on the ground to feel the three points of your foot touch the ground (heel, underneath big toe, underneath little toe).
I recommend ditching the running shoes while lifting so you can have a more stable base (which will help you get stronger over time!). Especially for exercises such as deadlifts, squats, rows, and other compound exercises that require stability from your feet to complete with proper form.
Lifting shoe recommendations:
If you needed an excuse to do a little shoppin', here it is!