HDMI video out vs. RGB for TV

I know very little about video in general so I'm wondering what, if anything other than audio on the same cable, I'm assuming, would be the advantage to using an HDMI cable over the old RS232 video and audio cables between a Dimension 9200 and a flat screen TV in our office?  This is a new construction office that I'm building the network for so, before the sheetrock goes up, I'm trying to keep the room clean by hiding as many of the wires as I can for the TV that will be mounted on the wall but will be essentially using the TV as a monitor for our "webinars".  The Dimension will need a video card with HDMI out so I was wondering if anyone could also suggest a newer video card that would fit this older PC?  The original video card is listed as "CARD (CIRCUIT), GRAPHICS, 7300, LOW ENCRYPTION, MRMGA10, 2" in the System Configuration so it has a port that will support an adapter/splitter for two screens.  Is this card enough to run the TV with a HDMI adapter?

Thanks.