I have just completed a *alliance RTW trip in business class.
Route:- EDI-LHR-YYZ-YVR-HNL-AKL-CNS// BNE-SIN-FRA-EDI. Airlines BD, AC, NZ, SQ, & LH.
Flying east to west 'following the sun' seems to help combat jet lag to some extent, in my opinion. - Note slightly longer flying times this way!
Take flights which are not scheduled with early morning departures or midnight arrivals, and if possible overnight flights! - avoiding overnight trans Pacific flights may not be possible.