How much does the resolution affect performance?

If you take a generic game and change resolution to 640 x 480, 1280 x 1024 and 1920 x 1080 respectively, how heavily would this affect performance?

Is resolution an important factor or rather neglectible when trying to find perfect settings for a non-high-end graphics-card?

It is (after switching AA off) the most important setting: doubling your resolution requires four times as many pixels to be updated per frame. So, as a rough estimate, by decreasing your resolution for a factor 1/f, your framerate can increase up to f².

You can actually answer that yourself. A graphics card has to calculate the value for every pixel from a series of functions.

Every resolution defines the available pixels on the screen (e.g. 640*480 = 307200). As the each resolution grows in both dimensions (width and height or x and y) this is a quadratic (x^2) function that grows faster than linear.

There are still other factors to consider, but the count of pixels is a very important factor for how fast your graphics card can calculate 1 frame.