The screen size depends on the usage of your computer. If you want to use for browsing, MSOffice etc. then a 14" or 15" screen is sufficient. If you watch lots of movies then better go for a screen larger than 17" with 16:9 aspect ratio.
The Screen quality depends on your budget. If you have good budget, go for full HD (1080i) resolution screens with LED backlit. The latest LED backlit screens provide brighter images with low power consumption. Otherwise you can go for a (720p) screen for low cost. It is better to get a matt finish screens which are antireflective rather than glossy finish.