instead of an lcd?
Eh, the only two types of monitor you can buy are CRT and LCD. CRT is the big chunky ass things that are basically no longer available. Everything else is an LCD.
1080p just refers to a specific resolution/refresh rate combination the monitor is capable of achieving.
1080p is by no means particular "good" when it comes to monitors, especially for gaming, where other factors such as response time, brightness and colour contrast matter much more than the exact resolution, since the size of each pixel is pretty much fixed, unlike CRT's which had a much finer pixel pitch (and still do) than LCD's. You also want a monitor that can handle at least 60Hz refresh rate, but preferably higher. 1080p might only be capable of doing 50Hz, which is partially what the "p" stands for.
Not all lcd monitors are 1080p capable. Most sub-20" monitors will not achieve the 1920x1080 resolution required. Even most 22" monitors won't as they are typically the cut-off between 1680x1050 and the 23/24" monitors that are 1920x1080 or 1920x1200
