A backend only machine is designed to sit somewhere and not necessarily ever need direct user input at the console. Depending on the tuner cards chosen, this machine doesn't necessarily have to be all that powerful. A backend only machine will require only about 2-3GB for the OS and won't have an X server installed. Setting up a backend only machine will require that the computer you remotely administer it from has an X server installed so that the initial setup (which does require X) can be performed over a network.
A frontend only machine typically is used for HTPC usage. It's preferable that such a machine is quiet, small and fits in will with a home theatre. A frontend only machine will have just enough installed to be used for a frontend. The entire Gnome or KDE environment isn't necessary, as it just provides bloat and wastes space and memory. It's usually a good idea to get a remote that is supported by lirc to use with this HTPC.
Combined Backend Frontend
A backend/frontend combo machine is the most common setup for people getting started with myth. It can be used as a HTPC for your home theatre, but it will always be on. Like the frontend only role, its not really necessary for an entire desktop environment. A light window manager will suffice, and keep this simplistic.
Frontend & Regular Desktop
A frontend and desktop machine is a machine that won't necessarily be on or run the frontend at all times. It makes sense to use an entire DE like Gnome or KDE for such a machine, and then only launch the mythfrontend when needed.
Backend & Regular Desktop
A backend and desktop machine is a machine that won't necessarily be used for frontend playback. The machine will simply perform backend tasks in the background from regular usage. If you already have setup a backend on your network, this machine can be a secondary machine possibly just used for performing jobs such as transcoding or commercial flagging.
Combined Backend, Frontend, & Regular Desktop
A backend/frontend/desktop machine is a machine that will be on at all times. The user may use it for desktop usage, but not always be running the frontend. The machine will do all of the scheduling, recording, commercial flagging and such in the background. If you were to compare this to a similar machine in the MS world, most MS MCE machines are of this nature. If you opt to do this, be sure to chose a tuner card that includes hardware encoding.