Mainly I believe they used the TYJ MK 1, but they also used the Newberry box for the scenes where the 2 boxes are seen together. I believe they altered the Newberry to make it look a bit more like the TYJ.
If you have a quick look through the TARDIS reference sections you will find plans for both.
Other things to remember are: make sure you seal any gaps in the wood first. Flexible sealer is best as it should move with the wood as it expands & contracts with the weather. Make sure the roof has a good slope on it.
Regular check ups to keep everything in order & prevent major problems occurring.
Finally, don't forget the base. Everyone worries about the roof, but in many cases it's the base that starts rotting first...
Since you asked, I'd say wood with a fiberglass overlay. My first roof was basic tar paper, stapled and glued on and then painted. It got the job done for a long time, but fiberglass is a lot simpler and more convenient that you'd think. Just get fiber cloth instead of non-oriented strand, lay it out, mix the resin and hardener, and slap the bugger on. It's easier than you'd think.
I've put this off for as long as I can, but now it's time for the part I've been dreading...
Should I make it out of wood? Cast it in fiberglass? How can I optimize it to be both lightweight and strong? These are the questions I have not yet found the answers to. I'll probably spend the next few days poring over various TARDIS builds looking for solutions, but I also wanted to ask you lovely folks if you have any suggestions, or links to previous builds with some tips and tricks. Also any advice for things I should definitely NOT do?