The fact that the system - for your described usage - connects to the TV is superfluous. You just need either a DVI to HDMI converter or a graphics card that supports HDMI out. Or your TV may have a VGA in, in which case, you really don't need anything special. Your primary concern is that it runs web video well enough. While I've run video on AMD K6 500 MHz CPUs years ago, most flash videos (what sites like hulu use) typically require beefier hardware. I would say just about any system should do. I'd stay away from an ATOM based system though - I tried using a dual core, hyper-threaded atom as my Media Center PC and it was JUST underpowered enough to not work appropriately. While you're not talking about using media center (I'll get to that in a moment), I've seen full screen flash videos being choppy on slower, slightly older hardware.
Now, media center - are you familiar with it? It's like TiVo from Microsoft - only it's free (part of the Home PRemium and later versions of Windows 7) and has no subscription costs. It doesn't record TV that it thinks you'll like (like TiVo), but otherwise, it is a DVR that, if you watch TV through it, offers instant-reply, it's own guide and the ability to select programs to record. It does require a tuner device (and supports up to 4 of each kind of device - digital, analog). I've been using one I build since December... it's great... I can't remember the last time I watched something that I hadn't recorded (outside of a baseball game in HD), I have over 500 programs stored waiting for me... so there's never "nothing on" for me to watch, nor is there a huge library of tapes and DVDs I've recorded taking up space... it's all on the one box witha 1 TB hard drive, connected to my 37" LCD TV.