Yes, there are a number of different connector options that bring out different sets of pins. Some only bring out power and CC (for devices that only need to charge), some bring out power, CC, and D+/D- for USB2.0 devices, others bring out all 24 pins for full functionality. Unless you're building a USB3.x device, you don't need all 24 pins and selecting a connector that only brings out what you need will make things much easier to route and assemble.
As far as the shield/shell, in general you should solidly connect it to your device's ground unless you have a specific reason not to. Some devices need additional care, but something like that board which just has one USB connection and then what looks like some GPIO should be fine with a solid connection. There are numerous threads here on the subject, pay particular attention to any of the replies where user T3sl4co1l has provided a wall of text, those are typically very helpful and insightful. Even if you have a specific reason to NOT do a direct connection to the circuit ground, generally you still want a mechanically solid connection to the board, so designing in some previsions for that are especially important on SMT connectors. SMT mechanical pads with no additional anchoring to the board will rip off very easily, so expanding the pad with a bit of a fill around it and putting some vias in/directly around the pad will help strengthen it.