There are several options for you...
I don't know of any Intel boards that have DVI out. I think there may be some for the OEM market, but I've never seen one for sale. I could be missing something. You'd probably have better luck looking for a Intel-using laptop with DVI-out.
For DVI out and other options you'd want to purchase a ADD2 card. I am told these work well with the GMA stuff. They are dumb adapters that plug into the PCI express port the motherboard.. Doing so sacrifices that PCI-E port and sacrificies the use of the onboard VGA-out. (so no trying to do dual monitors with a single DVI out on the ADD2 card and the onboard VGA) It's a pretty much direct connection to the onboard Intel stuff.
This is not to be confused with the old-style ADD adapters that were nothing but doggie poo-poo.
IF your intersted you may want to ask for more details on the Xorg mailing list.
DVI, being a digital pathway, has some serious bandwidth limitations... So that limited resolution is real. To get high resolutions cards will combine DVI channels to get the bandwidth needed for the resolutions. Most GMA stuff supports dual channels, but I don't know how all that would work. I don't know much about DVI... 1600x1200 maybe the max resolution that you can possibly get with combining channels. I just don't know.
Keep in mind that HDTV != digital. HDTV standard allows for both analog and digitial transmissions and provide high quality. So one real option is to purchase a VGA-to-Component adapter and get analog HD resolution that way.
If you purchase a high quality (expensive) adapter you can get very very good quality output. Very good. If you get a bad one then it'll be poor output and it'll not have hte adjustments that you'll find you'll need.
Also keep in mind that:
Composite = the single yellow plug = bad quality..
Componant = multiple plugs of different colors = good quality.
Now the sad part is that although the Intel hardware supports mpeg4 acceleration (XvMC) for decoding the Linux drivers do not support it as far as I know. There is XvMC support for older 'Extreme Blaster' i8xx devices, but no GMA support. This is different from just 'Xv'.. The 'MC' is for motion compensation and aids greatly in decoding media.
This is something you'd definately want for larger HD resolutions. Mythtv Wiki has more information on this sort of thing.
All in all you'd probably just be better off bying a mid-range Nvidia video card with proprietary drivers. Personally I'd rather have the open source drivers, but realisticly Nvidia is the obvious choice.