As far as greatest fights ever i cant help you there sadly as i have only started watching a year ago. But i would recommend you go into the K-1 video thread as im sure MLS had added them while he was here. Names to look out for would be Peter Aerts, Ernesto Hoost and Andy hug while in there as they all have great fights.
For the back ground info its best to read the History of K-1
There are 2 types of K-1 GP's. The first and oldest one is the K-1 World Grand Prix which focuses on HW-SHW fighters(past champions)
. Some notable fighters would be Remy Bonjasky, Peter Aerts, Badr Hari, Gokhan Saki, Melvin Manhoef, and Tyrone Spong.
The second type of K-1 GP's would be K-1 World MAX GP. MAX stands for Middleweight Artistic Xtreme. Notable fighters would be Albert Kraus, Masato, Buakaw Por.Pramuk, Andy Souwer and Artur Kyshenko
All of the fighters metioned are in the Video thread. Hope this helps you out.