I dunno about OSX, but my Linux Mini 9 (very similar to the 10v) can drive an external 1080p screen in addition to the onboard screen. 30in "monitors" tend to lack analog inputs and are usually higher resolution than 1080p. I expect they won't work optimally with a 9/10v, but a 30in "TV" should work (since it's gonna be 1080p or below).
But like I stated, I dunno about OSX.
As for watching TV, I'd recommend against relying on a TV tuner connected to the Mini. Performance might not be great. Instead, pay a couple bucks extra for a TV (instead of a simple monitor).
As for picking a screen, higher res TVs (1080p) should work better when used as a monitor, but that many pixels may be overkill, if only matched with a Mini.
There are also screens that straddle the line between TV and monitor, like the Samsung P2370HD. "Hybrid" TV/monitors have monitor features (high-resolution for their size, DVI and VGA inputs), but they also include TV tuners and other inputs, making them function as TVs as well. (I have the older, similar Samsung 2333HD).