Albatros C.I was basically an Albatros B type with a machine gun. Was superceded by the C.III around Spring of 1916. The C.III was the first two seater with a forward firing MG as well as a rear firing MG. Served until late 1916 when the C.V/16 started to apear. To all appearances the C.III was a good, solid aircraft that was well liked by its crews.
LVG C.I was another early war plane with a machine gun added. Served into early 1916 when the C.II came on line. The LVG C.I was a very stable and slow machine, not terribly well suited for combat.
Aviatik C.I ... same story

. Served into mid 1916 when it was replaced by the C.III. The C.III was really nothing more than a streamlined C.I, but the reduced drag added a nearly 18 MPH to its top speed. Also a slow, stable aircraft.
The Rumpler C.I was introduced (I think) around mid 1916 and served well into 1917. Good high altitude performance and handling characteristics made this one the best of the lot.
As for mission type they were all, to the best of my knowledge, general purpose two seaters. This means observation, artillery spotting, and maybe a bit of light bombing.