Question about picture size and auto-resizing background

Hi all,

I want to create a website with a background that will auto-resize according to the stage size using AS3.

But what i need to know before I do it is: What is the right resolution for the background picture?

I want people with resolution starting from 1024x768 to view the website correctly and I also want people with 24’’ monitors to view the background with good quality so I guess the image needs a high resolution. I started with 1936x1288 but when I resize the stage to fullscreen the bottom of the image gets cut off.