Have you ever seen the text from a Playstation or some other tv game on the TV? This is the quality you'll get. The best you can do is to buy a monitor with RBG input. This will give you the best quality. Remember the ones Commodore had(amiga)? This kind of monitor. The cheap tv card will give you similar quality or slightly worse.
The other solution that will work fine is to have a small tv (14in).
By the way, what do you mean that the tv monitor takes a lot of space? Your pcs monitor is smaller? Is it an LCD display or what?