The common monitor resolutions are 800x600, 1024x768 and higher. So what's the best resolution to use to fit all?

It is very tricky and there is none best solution for that. It is impossible to design a website to satisfy all resolutions.

What we recommend

Understand your customer profile, and choose the lowest resolution. Typically is 800x600 at the time of writing. You can use some of the online analytic tools to do profiling, or your Cpanel.