Should I prefer velcro, lace-up, or slipper shoes?
It's basically just a matter of personal preference.
Velcro shoes and slippers are great for getting on and off quickly. You'll usually see more aggressive shoes with velcro closures, not only because climbers are removing them after every climb, but because a velcro closure makes room for extra rubber to be added on top of the toe box, improving their capability while toe hooking.
Lace-up shoes will perform more comfortably in cracks and will feel more snug as the closure provides a more even pressure around the top of the foot.