It doesn't matter as long as you are below 20ms, and just about everything is. Response time is supposed to be the time it takes a pixel to go from black to white to black. There are 2 problems with this:
1) This is not real world, pixels usually go from one stage of gray to another stage of gray, so even if this were measured properly, it wouldn't be all that useful in real world applications, which leads me to point 2:
2) Its never measured consistently. Given the above, pretty much all monitor makers cheat, instead of a black to black response time they measure a grey to grey response time. Problem is there is no universal standard in terms of where to start and where to finish. The reality about LCD panels is there is a handful of panel makers and a lot of times you will find the same panel in different brands, or different panels within the same model. Often times you will find one brand touting a 5ms response time, another will have an 8ms response time and they will both have the same panel.
3) Most people confuse response time with lag, they are different things. Lag is how long it takes for the signal to go from your computer to get on your display, response time is just how fast the pixels change after the monitor tells them to change. So you can have a screen with good response time, but bad lag, and vice versa. Lag is a LOT harder to determine though, since nobody includes it in their specs.
Here's my take on it, and I have done a lot of research, but by no means am I a expert or an afficionado, but for what its worth here are my thoughts:
Just about any modern LCD screen will do, most of them are plenty good enough for MAME use. You don't have to worry about ms response times that much because most MAME games really don't play that fast, its not like you are doing modern fast twitch FPS games with a boat load of detail that needs to change quickly.
A lot of people say they like the way CRT's look better. I like the LCD look, and with different filters available, the casual player won't know the difference.
There is the whole IPS/PVA/TN thing with lcd screens. People cream their panties over IPS, Personally, I prefer PVA, but really, once again, it doesn't really matter for the applications we are using these things for: PLaying 8-24 bit games.
That's just my 2 cents, yeah, you can go out and spend 500 bucks on a brand new IPS monitor, but really a used 15 inch one built within the last 5 years will probably look just as nice to 99% of people, and you will save like $450.