Metre is the correct British spelling - it's not a "fancy pants" thing!
How do I find out the size and resolution of my laptop screen?
There are too many Americans in this forum, who believe their spelling is the correct one. Why can't we all standardize on the Queen's English?

Regarding how to find the resolution on your laptop: It depends on the OS (Mac/Windows/Linux/others), and on the OS version to some extent. On Windows 7, right-click on a blank spot on the desktop, and choose "Screen resolution". The current resolution (in pixels) is shown. It should match your laptop's hardware resolution, otherwise the text will be fuzzy. On a Mac, choose System Preferences - Display.
Regarding common resolutions in use today: On a laptop, you are pretty much stuck to the hardware resolution (often 1366 x 768 or 1600 x 900 on small laptops, bigger or more expensive laptops may have full HD (1920 x 1080) resolution).
On a desktop or external display, the most common resolution today is probably full HD (1920 x 1080), because this is what is most common in today's TV technology. In a few years, 4K resolution (3840 x 2160) will become common.
Higher resolution means you have room for more information. But it also means you need bigger screens, otherwise the displayed items will be too small. A full HD external monitor needs to be approx. 23" in size, whereas a 4K monitor probably should be 46" or even 55". That is, if you want to keep the current pixel size. So-called "retina displays" have smaller pixels, but then the software needs to scale up text and graphics, otherwise it would just be too small.