I'm not a fan of LCD's for classic gaming, one for the picture quality in low res games as you mentioned, and secondly because of the input lag. For example, the original Donkey Kong cabinet had a CRT, so when you pressed jump, Mario jumped relatively instantaneously. On a bad CRT, you won't see Mario will jump until several frames after you press the button. This is noticeable and can be very detrimental to gameplay.
Luckily, if you're absolutely set on one, there are low-lag LCD's out there. You can't beat a CRT, at least with current technology, but there are some LCD's with input lag under 1 frame, which is pretty good. Start with this list:
http://shoryuken.com/forum/index.php?threads/sub-1-frame-hdtv-monitor-input-lag-database.145141/Input lag should be your first concern for enjoyable gaming.
Next, you should first figure out if you want a 4:3 or 16:9/16:10 monitor. The latter will mostly be good for newer games while classic games would have be run in letterbox. I'm guessing you'll want to go with a 4:3 if you're focusing on the classics.
Finally, will the monitor be mounted horizontally or vertically? If you're limited most by the width of the cabinet, you might be able to fit a larger monitor if it's oriented vertically; and there are plenty of arcade games, especially in the 80's, that had vertical monitors. Horizontal games can run letterboxed of course.
Since LCD's have to benefit of being so light, you could also consider making it rotatable. You'll have to leave more space around the sides for it to turn though, so it may not actually give you a larger picture than going letterboxed on a larger monitor.