If eggs are the only reason for a non-stick pan, you can skip it. I make my eggs (omeletes, scrambled eggs, etc) in a tri-ply calphalon frying pan without much butter or oil (no more than .5 Tbsp) and cleanup is a breeze. The secret is to use room-temperature eggs (this is true of protein in general). If you don't have enough time to let your eggs warm up, just fill a bowl with warm tap water, put the eggs in and by the time you're done the rest of your prep the eggs are the right temp.

+1 on the rest of your recommendations though. A good knife and set of pans (all tri-ply or anodized aluminum) helped improve my cooking skills a lot.