C is common. However, one of the starter decks was the "C" deck so those cards also had a C (but it was much smaller).
C+ I'm not sure what cards you're seeing with C+
Roman numerals -- those actually stand for the set they are a part of. There are 26 sets of 10 ten cards.
R is for rare.
LR is for legacy rare -- these are cards that were re-released with updated wording and graphics.
UC is for uncommon--however only one expansion used this (Priests).
UR is for ultra rare.