You'll be controlling everything from the computer, so yes, you have to run to the computer every time you want to pause the show. I have a computer plugged into my TV, and my solution was to get a wireless keyboard and mouse, and control the computer from those, while they sit on the coffee table.
As for showing the computer screen on the TV, that's where it gets difficult. If you want to sit at your computer desk sometimes and sit on your couch sometimes, then you need a video card that will display on two screens at the same time. Plug your normal computer monitor into one, and plug your TV into the other. (I use a dedicated "media computer" to control the TV; using the same computer for both your TV and general sit-at-a-desk use is a little bit harder, but not too much.)
That brings up the next question: what input plugs can your TV take, and what output plugs does your video card have? If you're fantastically lucky, then you have a DVI output on your video card and a DVI input on your TV. You are probably not lucky. (Or you're like me, and abysmally
unlucky: I have a DVI input on my TV, but it only handles a single highly-specialized signal format that my computer can't make.)
Video card plugs (oldest to newest): VGA, S-Video, DVI, DisplayPort. VGA and DVI are both pretty common; DisplayPort isn't on everything yet.
TV plugs (oldest to newest): Composite (yellow RCA video cable, red/white RCA audio), S-video (yellow multi-pin video cable, red/white RCA audio again), component (red/blue/green RCA video cables, red/white RCA audio), DVI (lots of pins in a single cable, still needs red/white audio cables), HDMI (really flat plug, includes both video and audio) and DisplayPort (if you're lucky; will probably need red/white cables)
So you'll need a signal to go from your computer to your TV. Some plugs go straight over (S-Video, DVI, DisplayPort), and some don't (computers don't do composite, component, or HDMI). Here's a link to an EXAMPLE (haven't tried this one) VGA-to-component converter: http://www.google.com/products/catalog?hl=en&q=convert+VGA+to+component&um=1&ie=UTF-8&tbm=shop&cid=11721573182540550012&sa=X&ei=ZN8WUKjlKpO50QGayICYCw&ved=0CJUBEPMCMAc
And don't forget to run the audio over to the TV. This is more straightforward; almost all computer plugs are 3.5mm stereo cables, and almost all TV inputs are coaxial RCA cables. Here's a cable that goes from one to the other: http://www.google.com/products/catalog?hl=en&tok=6AOqHaaaCfAKAy-_Lw-jxQ&ds=sh&pq=rca+to+3.5mm&cp=18&gs_id=o&xhr=t&q=rca+to+3.5mm+cable&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&biw=1280&bih=896&um=1&ie=UTF-8&tbm=shop&cid=1889247817842361998&sa=X&ei=Bt4WUIbWJrHh0wH2q4DoCQ&sqi=2&ved=0CJMBEPMCMAM