If you're really sunk on this idea, it can be done. I do it,, but there are limitations and things to consider:
1. PC content. If you're going to be mostly browsing web sites and writing papers in Word, you can pretty much eliminate plasmas from the equation unless you go upto 65", because you'll be limited to 768 pixels vertically. On your 19" monitor, I'm guessing that it's got a resolution of 1280x1024 or something. Take a piece of paper and cover up the bottom 1/4 of the screen, and then slide it up a little more because you have to account for the Task Bar, and that's how much room you'll have. Personally, I don't think it's enough room to do very much. I mean, you'll be able to see it from plenty far away, but you'll probably feel constricted by the lack of space vertically. And possibly not know what to do with extra space horizontally... The exception is $5000 Pioneer PRO-HD1 which is 50". If you're willing to spend that kind of money, it's one heck of a tv, for sure. But if you're not, you're going to have to go LCD, specifically, one that has 1920x1080 resolution. A top of the line 52" from Sony will run you about $3700, and is also a marvel. You don't need to spend that much money, of course, on a 1080p monitor. You can grab a 37" Westinghouse for $1100, which works as a great monitor because you calibrate the color through the computer, but won't offer as good performance when it comes to TV, as you're limited by the TV's controls for calibration. In terms of sharpness, though, I can't imagine it being any sharper. It's a giant computer monitor... But here's the catch: (which brings me to the second caveat)
2. Viewing distance: The 1080 displays are SO sharp, that you'll be limited to a relatively close viewing distance. Sure, you can lower the resolution for the computer, but that defeats the purpose of getting a high-res lcd in the first place. Even with a 52" lcd, even with excellent vision, because of the density of pixels, I wouldn't expect to be able to view type and such comfortably more than 7' away, which if you actually get up and measure it, isn't very far. And that may be pushing it... But maybe you have eagle eyes. My guess is, though, that 12pt type will look like 9pt. It'll be sharp as a razor, but it'll still *appear* smaller than on your 19".
So if you can live with those conditions (and are willing to shell out an additional 25% if you plan on buying this at a store), then I would respectfully disagree with my colleagues here and say go for it. Otherwise, a TV card for you pc sounds like a much better idea.