Does an N64 look really bad on a flat screen TV?

I’m looking around for a good cheap flat screen TV, like 200–300 dollars. I found a couple at Best Buy that fit the bill. 29 to 32 inches. Insignia and RCA. Built in DVD and those red, white and yellow components I need for the N64, Gamecbue and PS2. See, I have this section of my room where I have my old video games, and I really need to replace the old bulky television badly.

However, the guy at Best Buy said that old video games would look terrible on a screen like that. I’m not sure he’s entirely correct. I remember playing games from the Gamecube and PS2 on hi-def screens back in college and they were fine. I’m not sure about the N64 though. What about even a Super Nintendo?