What is the best way to build a kitchen knife collection?
Buy a decent quality steel and sharpen the knives you have. 
Replace the ones that your are least comfortable / use the most first.

Essentials:
Chefs knife 8-10" blade pointy tip helps but not essential. (think mines about 8)
Pairing knife 3" pointy tip.
Knife w/ Serated edge. Think tomatoes, bread (big one for bread, little one for tomatoes/veg)

Next:
Filleting knife (ultra flexible, sharp skinning and filleting fish)
Boning knife (less flexible - almost stilleto like knife for dealing with carcass deboning - meat)

On:
Carving both meat and cured fish.