Your games are resolution independent, so don't worry about what the working resolution is for your monitor. The major concern in boosting your fps is your video card.
Regarding LCD vs. CRT, I've been using a NEC LCD1760NX for about 6 months now and I have overall positive feelings about it.
I went for a LCD not just because it was cool looking, but because LCDs are progressive scan as opposed to CRTs which use conventional interlaced images. What this all means is LCDs give you reduced flicker and less eye strain. Image quality is not as sharp as CRT but it's very very close. Colors are a little different, but once again this is a minor issue. Some LCDs are hard to view if you are not perpendicular to the screen and looking at it head on. So if you’re looking at porn, it makes it a little easier to not get caught.
On 19" vs. 17" be careful, you might get a monitor that's too big. The viewable area on LCDs is much greater than on CRTs. So your current 17" CRT is comparable to a 15" LCD. 19" LCDs are great for watch HD, but for gaming you might want to be a little closer and a 17" LCD will do just fine. Not to mention that it'll cost less and use less power.
Of course, I could be completely wrong...