With a width of 31" you'll be looking for a screen size of at least 30". LCD TV's only come in certain size steps so you'll have to check individual brands.
In my search for maximizing screen size, I found that Toshiba's had the smallest bezels and they've now introduced a super-thin bezel series. Where some brands I could only fit 50", with a Toshiba I could have gotten a 56".
Now, most owner's manuals recommend that you leave enough space around the TV for air circulation--usually about 4" around the sides and top. If you're going to put the TV in an enclosed space, you may not want it to fill then entire opening. I never discovered this until after I bought my first LCD, so I don't have the clearance on the sides, but luckily the top is open to dissipate heat. I did loose access to the side controls/inputs, though.
Last edited by Stargazer; 2007-12-10 at 05:54 PM.