Any desktop or laptop computer running Windows, Linux or OS X should fit. Since QRex is not a software itself but a specific organisation of the regular QGis/PostGIS tools, the hardware requirements are depending on the latter. For a basic use of QRex on the field a light laptop with an integrated GPS would be the best choice. It is advised to protect the laptop.
If the laptop doesn't contain an internal GPS, an external GPS can be connected and used with QGis. See QGis documentation for the installation. If no GPS is available, an aerial image can be used as a background reference for positioning.
It should also be possible to use a windows pro tablet but this has absolutely not been tested yet.