Does your computer support USB-C or thunderbolt? That would be the first question.
My latest MacBook Pro (work provided) has the USB-C ports, so I need to find either Thunderbolt-3 drives or drives that have the USB-C port on them. Of course, I can also use a USB-C to USB converter and make any drive work.
My Mac Pro and older MacBook Pros support Thunderbolt-2 as well as USB.
With thunderbolt drives typically being more expensive than their USB counterparts, I typically use Thunderbolt for drives that will be staying at my desk, and opt for USB drives that need to be portable.