You aren't the first person to consider this question. Here are a couple of other threads:
I have one of each. My main PC is hooked to a Viewsonic PF-815 (22" CRT, perfect flat Trinitron), while my second PC (where I am typing this now) is connected to a Hitachi CML-170SXWB (17" LCD, extra-wide viewing angle, built-in tinny stereo speakers).
My suggestion for gaming is to get a good
CRT. Look for a perfect-flat aperture grill (Trinitron/Diamondtron) CRT that will display the optimum resolution at a refresh of at least 80Hz, preferably even higher. For 19" CRTs, that's usually 1280x1024, while 21-22" CRTs may be very good at 1600x1200. High-end monitors with good electronics may have enough bandwidth to display higher resolutions, but the number of physical pixels will usually match those. Of course, if you run a CRT at a resolution other than its recommended one, it will look a lot better than an LCD will look at something other than its native resolution.
For stuff that runs on the Windows desktop and for 2D strategy games (e.g.: Warlords Battlecry II), the LCD is very nice, provided that you run at the native resolution. For most 17-18" monitors, that is 1280x1024. Unfortunately, the Voodoo5-5500 in my second PC won't drive most 3D games at acceptable framerates at that resolution. Even if it would, the LCD leaves trails. You can even see this on fast-moving action scenes when playing DVDs. The LCD pixels cannot change state as fast as 60 or 75Hz. Your mileage may vary. Some LCDs are faster than the NEC/Hitachi technology in my screen, but many of those have a much narrower viewing angle than than the NEC/Hitachi technology.
If you really want to use an LCD for gaming, consider how the native resolution of the screen matches the games that you want to play. The scaling artifacts can vary anywhere from ugly to almost unreadable. Again, your mileage may vary. Some LCDs may have slightly more sophisticated scaling algorithms than mine.
19" CRTs are probably the best value. You can get a decent enough one for under $250, or you can get a top-of-the line model for a little under $400. A 17-18" LCD is going to cost about twice as much as a 19" CRT, with about the same viewable area.
A good 0.24 or 0.25mm resolution 22" monitor like the NEC-Mitsubishi FP1375X or Viewsonic P225f goes for $700-$1000, which is about the same price as a 17-18" LCD. The 0.22mm resolution 22" Sony GDM-F520f has a rather exciting $1450 price tag, but it's still cheaper than a good 20" LCD.