1980-1983 : From the early gigs with Hooky trying to sing Mesh, to the early live experiments with keyboards. The early performances of Chosen Times, Everything's Gone Green, Temptation, 586, Blue Monday, Confusion and Thieves Like Us are the things I like the most about New Order. My favourite New Order moment ever is the live video of Everything's Gone Green, a glorious mess.
Anyway what followed was great too, they couldn't stay at that early stage, they had to evolve and they did it making stuff like Low Life, Brotherhood and True Faith.
Then came another great period, 1988-1990, which saw them at their full potential. Fine Time, Vanishing Point and World In Motion, and some concerts of that period, show a band at the top, moving gracefully into a new scene they somehow helped to create, making big tunes and scoring chart hits. They were the Oasis of the late 80s, only they weren't shit at all! :)
Then came a lot of problems, but two glorious comebacks in 1993 and 1998, showing them ageing gracefully and sounding indeed fresher than the most of the young wankers out there. 