During WWII the Germans used several different styles of canteens, in two different sizes. All branches of the German Armed forces used them. There were no specific models or colors for any type of unit. (The blue covers you see are not Luftwaffe- they are 1950's Berlin Police.) The majority of canteens had a capacity of .75 liters. A larger, 1 liter model was also made.
The canteens consisted of a metal flask, metal or plastic cup, a strap assembly and wool felt cover. There were also "coconut" canteens which had the flask enclosed in bakelite rather than having a felt cover.
Metal flasks and cups were made of aluminum until late 1943, when enameled steel began to appear. Plastic (bakelite) cups were used throughout the War- most were black, but orange and green exist. It appears that 1 liter canteens were normally issued with the bakelite cups; the metal cup doesn't fit very well on the shoulders of the larger flask. There is also a metal cup similar in size and shape to the bakelite ones.
Leather canteen straps were usually black, but brown ones are occasionally found. Late War straps were often thin pigskin, and sometimes riveted rather than stitched. Web straps came in several configurations, in several shades of tan, green or gray. Despite collector and reenactor myth, web straps were not exclusively "tropical". They appeared in all theaters- as did the "coconut" canteens. They are simply less common.
German canteens have been one of the most vexing and difficult things to have reproduced. The minimum quantity requirements for the flask and cup are very high- we have been trying for years to do these.
Currently, there are several reproductions of the .75 liter M31 canteen on the market, most Chinese-made. They range from utter abominations, to decent quality, but none are excellent. The biggest shortcomings are the covers and straps. We have the best straps available- we are one of the only companies to use good quality cowhide and add the rawhide reinforcement to the piece that holds the hook. The crappy straps sold by nearly everyone else will not hold up. We now (2016) have basically perfected the covers as well. So, we are using our straps and parts from two other companies to assemble our canteens. This is why they cost more than some of the others. These are clean, the straps won't break and they look good.
To date, I know of no reproduction 1 liter canteens.
Original canteens can be used, so long as you replace the straps. 65 year old leather won't last long. Also, avoid the steel flasks- they are usually rusty inside and who knows what sort of side-effects can come from WWII German enamel flakes.