What is the optimal radius of gaussian distribution for determining pixel colour?
I'm not sure that there's a truly optimal radius&mdash;it's going to be a subjective matter based on what the image looks like.  As you say, too large a radius results in blurring and too small a radius results in aliasing.

I like to set sigma = 0.5 px, so that the overall radius is about 1.5 px (since the Gaussian has the majority of its weight within ±3 sigma of its mean).  In my experience that gives a good trade-off between blurring and aliasing, but that's just my taste, not based on any objective considerations.

By the way, as part of a blog post on antialiasing I wrote last year (which was based on an answer I posted on the previous incarnation of this site!), I tested a variety of antialiasing kernels against a synthetic test image and came out with 0.5 px Gaussian as my subjective favorite.