Remote Desktop will indeed do what you're looking for, i.e. mirror your HTPC screen on another computer. It may be slow though (it will lag a bit), and windowed applications (designed for mouse and keyboard) may not be easy to use. It completely depends on what applications you are using.
Remote Desktop (the official Micrososft app) I think requires a Pro version of Windows on your PC, but there is a third party one called Splashtop which works extremely well.
Talking about MC in particular, Standard View may be awkward to use with a touch device, Theater View is a lot easier but is really designed for a keyboard and/or remote control. But there are native tablet apps that don't need remote desktop: JRemote for iOS is probably the best MC remote, there is also Gizmo on Android, and WebGizmo that can work in any browser.