MRdumful | 62 points
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This order here covers various incarnations of the Justice League such as the Giffen/Dematties run and the Grant Morrison run.
It starts at the crossover "Crisis on Infinite Earths" which is meant to serve as an introduction to the large DC Universe. It ends at the James Robinson run just before the New 52.
There are several starting points if you do not want to read the entire order.
I decided to leave out certain titles that are related to the Justice League (Captain Atom, Animal Man, Mister Miracle, etc) with the exception of certain crossovers and miniseries so that the order is as Justice League centric as possible.
Other reading orders can be found here