Is my onboard sound good enough for PC 360's?

http://www.realtek.com.tw/products/productsView.aspx?Langid=1&PFid=28&Level=5&Conn=4&ProdID=173

I'm not sure what you mean by "doesn't support Dolby Digital sound..."; I've never heard of a single game that doesn't work with this Realtek ALC889 chip.

General:
The ALC889 is fairly good quality. After using my good sound card however, the quality of even the latest Realtek chips isn't good enough for me. Assuming your headphones are good enough (I can speak to my M-Audio AV40 speakers only) you'll notice a big difference especially at the lower frequencies where sound can appear more MUFFLED on the cheaper sound solutions.

A $30 or great sound card is likely to provide superior sound than onboard. It can sometimes be difficult to find TWO audio outputs (one for desktop speakers and one for headphones). Some speakers allow the headphones to be hooked up to them, but they have to be ON and can add a lot of heat.

*I prefer to have my speakers and headphones BOTH attached to my Auzentech X-Fi Forte sound card. I use an extension cable for the headphones and simply UNPLUG it when not needed.

I had SURROUND SOUND headphones with VOLUME control and simply turned the volume down when not using them. I had STEREO SPEAKERS though so I had to remember to toggle from Stereo to 5.1 Surround when putting on my headphones (and turn off the speakers).

MODEL:
ASUS makes good sound cards. I like my Auzentech X-Fi Forte. Creative is okay, but READ REVIEWS as I read about issues with some of their recent cards.

CHECKLIST:
1. Budget ($30 to $130)?
2. handle TWO outputs?
3. Headphone amplifier on sound card?
4. REVIEWS, REVIEWS, REVIEWS (Customer and Professional)
5. PCI or PCIe (just depends what you have unused on motherboard. Likely PCIe)

**If you have STEREO desktop speakers you can hookup the headphones to the sound card and use a SPLITTER for the green, front output.

REVIEWS:
http://techreport.com/review/23358/asus-budget-xonar-dgx-and-dsx-sound-cards-reviewed/11

http://sound-cards-review.toptenreviews.com/

Recommended card:
I couldn't even find my Auzentech X-Fi Forte, but for $75 this card MAY be a good choice if it suits your needs:
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=1766713&CatId=2769

At $30 the Sound Blaster SE is probably getting pretty dated as it's been out for quite a few years. Realtek may be lower quality than most sound cards but they do periodically come out with new audio chips so careful when comparing.