My favorite period of Amon Amarth is from Versus the World through With Oden On Our Side. I think that's all I'd really need to satisfy the urge to listen to AA. This may be because that is the time period that I got into the band, but I also think it's when they fully developed their trademark sound.
Having said that, early Amon Amarth had a distinct sound which was also very good and deserves attention. The first couple/few AA releases had more of that early Melodic Death Metal sound like very early In Flames but also with some blackened traits. Versus the World retained elements of the early AA sound but was the next clear evolution where they streamlined their songwriting, Hegg incorporated more guttural type vocals, and they achieved a more polished sound. Fate of Norns really accelerated this process, but I think they fully developed their new style on With Oden On Our Side. I'm not too familiar with AA after that point but my understanding is that the following albums were basically attempts to re-create that sound with varying success (generally less).
So, the peaks of Amon Amarth's development I'd say are: Once Sent From the Golden Hall, Versus the World, and With Oden On Our Side.