Teutonic HAMMER TIME!!!!!!
Lol, yes, the Teutonic Order was originally the German branch of the Hospitaliers. After displaying some of that epic-flavored badassery that would characterize them for the next 4 centuries at the Siege of Acre (1190) they became their own order of German Knights (Although still technically a branch of the Hospitaliers). When the Prussian and Lithuanian pagans took up the game of "Rape Pillage and Murder Polish Christians" professionally, the Pope gave them full independence and transferred their primary theatre of operations to the Baltic in 1232 (Though their capital was still located in Acre, so they still served militarily in the holy land). By 1250 the Lithuanians were on the run, and the Prussians were utterly broken, so the German Emperor granted them the right to bear the Imperial Eagle (in escutcheon) upon the Sable Cross Potent which the Pope had already bestowed upon them. The French King granted them the Or Cross Flory, all of which the Hochmeister bears as his personal insignia.
After the loss of Outremer (and their HQ in Acre) their HQ was or for a while located in Venice, but was transferred to Marienburg.
Due to the Poles request that any lands taken by The Order belong to (and thus bear the responsibility of holding) The Order, they gathered a land empire that rivaled any European king, and their military might was unchallenged.
Their era of most power was during the 14th century. Then their combination of supreme military might, Huge "Tracts of Land" and access to several Baltic Sea ports (Due to the fact that they happened to own one of the Coasts!) Really started to wig out the poles. (the guys who asked them to be there in the first place)
So they (the poles) thought it would be a good time for sneaky negotiations, and met with the Grand Duke of the Lithuanians and Allied with them against the Teutonic Order. While this was going on, the Teutonic Order was busy dealing with Novgorod and the Estonians. (Three front war!!!! Wooo!)
Even after Tannenburg (1410) the order maintained a powerful presence in the Baltic, and remained so until a Hochmeister converted to protestantism in 1525 and basically gave away all rights to their land after dispersing The Order's military forces to remote locations. They actually still exist and are in Communion with the Vatican (Still a legitimate order) today.
As far as kit goes, you can almost portray anything! With the gigantic time frame to work with especially.
You also can be afforded some abnormalities as Teutonic Knights had a tendency for lighter armouring (for all the raiding) and the complete melting pot of styles (German and Eastern European)