Which type of LCD screen is the best for gaming on the Amiga?

[jj]

Short answer: None. Always use a CRT video monitor for smooth scrolling. Even non-video CRT ones aren't as good (e.g. good VGA ones) because they're usually meant to be run at 85-100 hz, so the persistence of their phosphor is lower, giving a more dark/dim image (not always satisfactorily compensated for via the monitor's settings).
An old CGA monitor from the PC world would work OK too.

Now, if you're set on an LCD:

1. You need proper 50 Hz support. That's not optional. So both your scandoubler AND the LCD monitor must PROPERLY support 50 Hz
What is "improper" support of 50 Hz? It's "accept a 50 Hz input but upconvert it to 60 Hz".
A scandoubler might do that to ensure the output always falls in the VESA standards range. Result: Jerkiness
A monitor might do that because its display is fixed for 60 Hz. Result: Jerkiness

2. You need a ridiculously low pixel response time to avoid the inherent ghosting/blurring LCDs exhibit with moving/scrolling images. If we loosely translate PAL blanking time into pixel response time, it's in the 1 ms or lower range. There exist monitors that fast but that's still not ridiculous enough, don't expect CRT perfection. Plus, these monitors are rather new, so there's a big question regarding their 50 hz support. And they're typically wide ones, no 4:3 or 5:4 there.
For the tried and true ones, the 4-5 ms they usually spec for WILL give motion ghosting. My 4 ms LGs certainly show it, especially with moving dithered/highly textured patterns (an LCD screen's worst nightmare).


So:
If your scandoubler can do 1:1, you don't need 15 Khz support from the monitor. Just proper 50 Hz support.
An example I can give is my old LG Flatron L1932P monitors, they do 50 Hz fine but at 4 ms motion is just acceptably clear, not crystal clear as on a video CRT.
If it can't do 1:1, throw it away and either get a better one (for maximum flexibility when picking monitors) or look for monitors that apart from 50 hz vertical they also support 15 Khz horizontal, such as some Benq models (BL702A, BL902A, BL912 IIRC). This wiki has a more extensive list.

I guess a lot of this is not so much of an issue if your on an NSTC amiga though ?