An interesting new paper concerning a professional 500 Kv Tesla coil gives us precious information on how to design the coils:
Transformer form: Flat spiral with peripheral excitation gives the largest coupling factor.
Number of turns in secondary: Coupling reduces with increasing the number of turns. One turn primary and minimum number of turns in secondary (enough to give the desired step-up voltage coefficient) should be used.
Conductor cross section shape: Strip conductors give larger coupling than round conductors. A compromise between high voltage performance and coupling should be found.
Conductor dimensions: Wider strips give stronger coupling.
Transformer diameter: Larger diameter gives larger coupling. A compromise between transformer inductance (speed) and coupling should be found.
http://fr.arxiv.org/abs/1109.3081
Interesting paper. And you're right: It's a research paper geared to an audience of academics and/or professionals.
I went looking for other references:
http://www.docstoc.com/docs/7858010/Step-By-Step-Plans-to-Building-a-250000-Volt-Tesla-Coil-%28REVISED-VERSION%29
Not as big. And you have to pay for the article/book.
http://www.bunkerofdoom.com/lit/bigtc.pdf
This is free and tutorial.
Amazing1.com sells the plans to a 3 MV Van de Graf generator, but that's for the very, very serious experimenter.
http://amazing1.com/plans-all.htm
--Lee