Countertop faucets require space on the countertop between the sink and the wall, while those mounted on the sink save you that precious surface area. It can mean the difference between being able to fit in a tight sink or not.
If your mirror is centered above the sink, mount fixtures just a few inches to the left and right of the mirror. It should be as close to your face as possible.
Either way, whether your bathroom storage woes are centered around safety or convenience, you may like to reconsider regular doors in favor of ones that lift or slide up, like the lift-up mirrored panel pictured here. Some pull-up door systems are also semiautomatic for added functionality and user friendly appeal.
OK, technically this is in a laundry room, but this durable glazed steel bucket sink would work just as well in a bathroom, especially a guest or kids’ bath. There are no holes for a faucet, so you’d have to incorporate a wall-mounted one, as shown earlier. But hey, it’s two great ideas in one.