I have a Mini 9 and 1012, both running Linux. The 9 is different hardware, but not very. Here are my opinions.
Many HDTVs have VGA inputs. You just need a cable. If the TV doesn't have VGA in, a expensive adapter would work
As for resolution, the 1012 should be able to drive even the highest resolution TVs (1080p: 1920x1080). Physical size doesn't matter.
The main problem I foresee is getting the screen running perfectly at the native resolution. HDTVs don't always report their resolutions correctly via EDID (especially "720p" HDTVs), so it can take some work to get it running perfectly. My desktop's ATI graphics make it easy to override incorrect TV reports, I don't think Intel makes it as easy (but I'm not sure about the newest Windows drivers).
Over VGA, you shouldn't have any problems with overscan (picture "too big" to fit onscreen).
Finally, if you're only using the HDTV to display videos, then a perfectly configured display is less important. A perfect display is important if you're actually using it as a monitor.