What is the best fuel to use?

I would not use charcol bricketts. Too much ash.  Lump charcoal is best suited for the egg.  Check out Nakedwhiz website for info on different brands.  I don't think using logs or lots of wood chunks would work as well either. Using a few chunks for smokeing is fine and very common.

Yeah, your question should be "What brand of lump is best?"

briquettes were designed to burn at a continuous medium/high heat and rate, and cooking over them generally requires all the briquettes to be lit or ashed over.  you may not want to wait that long, or may not need that much fire.

the bigger issue is that they generate ridiculous amounts of ash.  that ash blocks airflow and will leave you tending a cooker whose very reason for being is to minimize tending.

as for wood as a fuel source... the reason charcoal is used as a fuel source is simply that it burns at a controlled rate.  wood is comparatively 'impure'.  lots of water and other organic stuff which needs to burn off before you can get an efficient fire.

if you burnt the wood outside the egg, down to coals, and then fed those coals into the egg, maybe.  but that's way too much effort.

charcoal is a refined fuel of sorts.  burning wood itself is like trying to use crude oil in your car instead of gasoline.  much more smoke, inefficient, all while gumming up the works. 

I use Royal Oak brand available at Wal Mart.  It's made by the same manufacturer as the Green Egg brand.  Very affordable and constant results.