You want a micro that has built in USB device functionality, many PICs do, some 8051 variants may, but I have not used those parts for many years.
Further, USB is somewhat complicated, so it is really helpful to have a library available that already contains the state machine to run the USB transactions.
A HID descriptor is a block of data that describes a human interface device to the PC, see chapter 9 of the USB specification. Getting the various descriptors correct is a big part making USB enumeration work (Top tip, linux gives more useful error messages here then windows does, and lsusb -v is most helpful).
Pretty much any USB device contains a micro of some sort, it may be mask programmed but it will be there, as it is by far the easiest way to implement the required state machine.
Regards, Dan.