For connecting your Mini to your HDTV, I would just use the display port/DVI and get an adapter (DVI/HDMI) to connect the video. Then use a separate connection for the audio directly the TV. If your TV as a toslink input, that would be golden, otherwise use use the L/R composite inputs. It's not like you're going to tell a difference of analog or digital stereo sound. If you ever decide to hook up to an AVR or something to give your 5.1 or more audio, then I would look into toslink adapter. Using the HDMI 1.3 connection just gives you one cable, but nothing more in your situation because the Mini you have does NOT support HD audio.
You can get all the adapters mentioned above at Monoprice on the cheap; probably only cost in the $3 to $5 for each piece, maybe cheaper.
I have a late 2009 Mac Mini, non-server. When I first got it, I temporarily hooked it up to a Vizio 32" HDTV, thus I speak from experience:
These pictures show the connections out of the Mini.
In case you're not able to tell, on the Mini, from top to bottom, power, mini-display port, 3.5mm auido. The audio cable is a 3.5mm to dual RCA/composite.
Luckily for you, more than likely, your TV will be able to detect that you've connected a Mac Mini and will set it to a proper native resolution, and will be really close to filling the whole screen. You may have to play with over scanning; I did. Things get more interesting, to say it nicely, when you're trying to use older home theater equipment.