Connecting a flat screen

I just got a Syncmaster 225MW 22" flat screen for my computer, up to now I was using a 19" CRT. So I unpack everything, start to connect the PC to the screen, and notice that the only video cable is a VGA cable. Now my Geforce 8800 GTS 640 MB only has DVI out, but came with a DVI to VGA adapter, and I can connect the PC with the screen just fine and it works. But somewhere it bugs me, and I wonder whether I would get a better image if the connection were totally digital.

So I go out and try to buy a DVI to DVI cable. No luck, none of the four stores I visit has one. But the last store sells me a DVI to HDMI cable, and promises me that this would work as well, as the screen also has a HDMI port. Well, first of all it isn't that easy, you need to push the "source" button on the screen a couple of times until he detects the signal from the PC via the DVI to HDMI cable. And then the image is much worse than before: it is bigger than the screen and not centered, so I'm losing part of the image. And it's far more blurry than the result I get with the cheap VGA cable.

Searching on Google didn't find anything, except complaints by other people that their HDTV isn't running well with their PC. The manual of the Syncmaster is silent on the issue, except saying that "you can't use a HDMI cable to connect a PC", but that might be a reference to HDMI to HDMI cables. The NVidia Settings screen, even in advanced mode, has nothing on DVI or HDMI. I'm stumped.

Anyone know whether I can use a DVI to HDMI cable to connect a flat screen to my PC? And is it even worth it? Should I buy a DVI to DVI cable, provided I can find one, or is the VGA cable going to give me the best result?