Everyone in ARMA starts their studies with the longsword, which is characterized as having both a long grip and a long blade. Often they are light enough to be used with one hand, but best controlled with two hands. These are not to be confused with true two-handers - doppelhanders, bidenhanders, zweihanders, schlachterschwerters. See this article for more info about sword types -
http://www.thearma.org/terms4.htm#Sword%20Parts
The reason for this? The study of the longsword is the key to unlocking the martial content of the our source literature. While the masters agree that all fighting is based on ringen (wrestling) they found the key to the art of fighting to be in the use of the longsword.
I'm too hungry to search for quotes right now.
BTW - many of us in the ARMA fight with weapons other than the longsword, however the basis of our armatura is blossfechten with the longsword.