What would be the best surf board to build for a beginner/intermediate surfer?

For a beginner/intermediate surfer you want a surfboard that is wide (around 22"+) for lateral stability and the longer the length the easier it is to paddle fast to catch waves. Not to say you can't start on a wide shortboard but it's just easier to paddling and glide into a wave then to have to jump up and set you feet perfectly in a split second on a shortboard. 

Board thickness really depends on your weight and determines total volume of the board. Thicker (2 3/4"+) provides more float and easier paddling, thinner boards will sink more and are geared towards more high performance surfing. 

A standard tri fin setup is good to start on. It provides stability as well as great turning ability.