DVI or HDMI would work the best in most cases. All remotely recent (like GeForce 4MX or newer) PC video cards are capable outputting HDTV modes over their DVI ports. If you have a DVI connector on your TV, get a DVI-DVI cable. If you only have HDMI, get a DVI-HDMI cable. HDMI and DVI are electrically compatible, but use different connectors. DVI is more common in the PC world, but the AV world has seemed to decide upon HDMI.
I use a FX5200 on my HTPC since it does the hardware accleration I need for HDTV decoding just fine, and it was cheap. Basically, anything that has DVI is likely to work.
In many cases, the TV will tell your OS what modes it likes, and you can pick whatever is native for your TV (1920x1080 for 1080p, 1280x720 for 720p). In some cases, it won't report things correctly (and may even send outright bogus data), and you'll have to be a little more forceful. If you run Linux, google for "HDTV modelines" for a way to force X to run how you like. In Windows, I guess try PowerStrip.
Note that when you are running native resolution, the outside 10% or so of the screen will be invisible. This is normal in the TV world and is called overscan. PCs, however, usually draw the desktop all the way to the edges of the imaged area. This can cause problems with things like invisible toolbars. Some TVs have an option to crush the image back down, but this uses software scaling, often producing notable artifacts. Avoid using this scaling feature if you can. On CRTs you can adjust this back out (usually in service mode), but not on discrete pixel technologies such as DLP, LCD, Plasma, SXRD/LCOS, etc., so you'll just have to live with either the overscan or the scaling. If the scaling is objectionable, you may have luck feeding it a slightly lower resolution, possibly down to the next TV standard mode, and having the TV scale back up.
DVI and HDMI are all digital, so there will be no reclocking going on and no analog issues. For short runs, cable quality isn't overly important (I've used 99c cables with good success). Most TVs will also accept any mode from 480i (standard res) to their native res or 1080i, whichever is higher and scale decently.
Note that all DLPs I've found lag. I'm guessing this has to do with the scalers TI recommends/requires when you decide to use DLP. The lag isn't overly horrible, but it is noticible on timing sensitive things like fighters and music games. Picture quality is amazing, though.
Many TVs have a "VGA" PC input. Avoid using it. The TV will often make assumptions about the mode this port runs and scale things in terrible ways, often not even preserving aspect ratio. DVI will usually give a superior picture anyway (if there's any different).
(Something tells me I just told you way more than you wanted to know)