Need a sound solution.

What sort of audio is built into the motherboard - what audio outputs does it include?

Look for a used AV receiver with either of those digital connectors - basically a mid- to hi- end AVR that handled digital surround sound as it can almost certainly handle DVD-A (96 kHz/24 bit). The sweet spot would probably be something that originally sold for $400+ but is being replaced by its owner because it supports too few or no HDMI connections. You should check the manuals online before buying just to be safe.

As a bonus (as in not required!), look for pre outs or (tape) monitor outs; gives you the option of adding a headphone amp at a later date.

Yes. Moving the digital-to-analog conversion out of the PC should help with background noise; and the DACs in these older AV receivers are better than one might imagine. There are still plenty of other things that can cause noise, but that is a story best told by someone with more knowledge than I.

Here is an example from the Los Angeles edition of Craigslist. While it is not as high-end as I might have hoped, I only spent five minutes looking . . . and the Onkyo TX-SR503 does have the features I would be looking for. I like the features-for-the-buck with Onkyo, and have owned two over the past six years or so (one 5xx or 6xx series and the SR706 that I own now). However, any of name brands should do: Pioneer, Denon, etc.

Since you are at school, you may be able to get some deals this time of year as folk sell stuff off to pay for summer vacations or whatever.