The classic cycling jersey has three rear pockets. With a little organisation and if you're not trying to carry too much or can move some of your kit to one of the best bike saddlebags, that should be adequate for most day rides.  Look out for pockets that are deep enough that items won't fall out if you do have to load up and that avoid pocket sag under heavy loads.
A zipped valuables pocket is useful, to keep keys and money safe as you are riding.
With the increased popularity of ultra-endurance and gravel riding, jerseys have sprung up that add lots more carrying capacity. Even if you're not contemplating a huge ride, just having somewhere separate to keep used food wrappers away from your other items is really useful and avoids mess.