3 choices- barefoot, flats, or a heeled shoe (heel is higher than forefoot)
barefoot- i tried it once deadlifting to shorten the pull n found it not to my personal liking. i found my foot trying to wrap the ground
like ur hands trying to grab a bar
-otherwise i have no issues, or know pros or cons on it.
-tried wrestling shoes which is a soft sole, but too much medial n lateral roll in the foot for me... didnt feel stable
flats -such as chuck taylors, shift ur center of gravity backwards promoting ur posterior chain
-chucks worked great for me for a couple decades. just switched to asics tokuten which i really like... same flat base but
less rubber on base thus producing a shorter pull, n more comfy
heeled -such as crosstrainer, runner, or boot, shifts ur center of gravity forward making more use of ur quads
so it depends what u r trying to achieve. i switch it up sometimes depending on my weak link and/or injury. u might consider a shoe with a solid base n not too squishy like soft running shoes and the fad reebok crossfit shoes. too soft a base will absorb all the kinetic energy n not leave as much in the elastic rebound. thats why weightlifting shoes have a hard base as opposed to squatting on a sponge. of course bar placement n range of motion will affect what muscle groups u target also. but i love box squats. just my 2 cents.