I'd like this to be a thread where we can discuss the pros and cons of various pens for use with eggbot.
To start the ball rolling, here's a comparison between two marker brands. The brand on the left, "120 markers", came from Amazon and had a wonderful range of colors (120 of them!). The brand on the right is Sharpie Ultra Fine, except the blue interior fill of the crescent moon is from the "120 markers".
Though the "120 marker" pens seemed to write on paper OK and initially appeared OK on the egg, eventually this water-based ink seemed to diffuse through the shell into nearby areas and resulted in a rather soft and messy image. The lines which appear bluish in the sun are from the black pen. It also takes much more time to dry - the smudges are from my fat fingers.
The Sharpies are darn near perfect in every respect, as long as the limitations on pen tip width and color selection don't bother you. I find that about 25% of the colors need considerable coaxing for the ink to start flowing.
I hope others will post other pen observations and images here! 8^)