Summary of my own RTW plans:
* Start in LHR because of cheap fare
* I want to start with AA Platinum challenge, therefore going westward.
* First flights are on AA only, to get 10000 miles ASAP
* After challenge there are 3 airlines that credit 200% miles to AA for class L: AA, LA, AY. All others credit 70% or less!
* Therefore my complete itinerary is:
LHR-LAX on AA
6 hops in USA on AA
JFK-HKG on AA (CX codeshare, but counts as AA)
3 hops in Asia on Japan (70% only) (HKG-NRT-SIN-NRT ?)
NRT-HEL on AY
HEL-LIS-HEL on AY for maximizing miles
HEL-MAD on AY
MAD-LHR on LA codeshare -- unfortunately I cannot book this in online tool

Total mileage credited will be 67000+
If I had the challenge done, it would be approx. 10000 miles more.

And all of this has taxes less than 300 GBP, because I started with AA.