King of the common codes is byf 44. Other common codes include byf 43, dot 1944, dou.44, and bcd 4. There is a list of codes by production estimate in the book Backbone of the Wehrmacht. It is interesting but if you use it be aware that some of the assumptions used to come up with the production estimates were wrong and this means that some of the production estimates are wrong there. This mostly affected the estimates from the years 1943-45.
Regarding rare codes, there are two codes which weren't recognized in that book as they were discovered after the book was written: swjXE (5 known) and bSw 1936 (1 known). Other rare/uncommon codes include S/27G, S/243G, 337 1939, S/42K, S/147K, S/237 1936, S/27 1936, and 660 1939. Note that other than swjXE which was manufactured in 1945, all the other uncommon codes were manufactured the first year the war started or earlier and this makes them even more difficult to find because of attrition. There are other uncommon variants and sub-variants like SS marked rifles, dual codes, district assembled rifles, commercial assembled rifles, and many more, but they are a bit more difficult to characterize in terms of accurate production estimates.