Highly recommend the drawstring bag. This one in particular is fairly cheap and hasn't failed me for over 4+ years of regular use for the gym and vacations.
It's got some mesh pockets on the outside for small water bottles and portable chargers as well as a zipper pocket for things like keys, or clutches. The main pocket has enough room for my men's size 10.5 sneakers. It'll take care of what you need it to without being super bulky.