It has no point to use your puter on a shitty TV screen... the money you will save over a good monitor will be spent (in fact 10 times more) to your occulist...
A cheap but decent display 17" monitor screen costs currently 100 $, which is not that much, is it?
And the "lines you mentioned are obviously the synch problems between your card frequwency and the refresh rate of your TV screen. You cannot expect anything decent from 50Hz or pseudo-100Hz refresh rates.
The above el cheapo 17 inch monitors offer a comfortable 1024X768 at 85 Hz refresh rate, which is more than enough to cut out any flickering or transistion effects.
If your family room is ugly with a monitor inside, you can always get a divorce...
For one thing, I have my puter and NO TV screen at my living room- Master can confirm it!