Thanks to a large mintage, the 1883 Indian Head Cent is a very common coin. The population profile matches that of the 1882 Cent almost identically, across all colors designations and all grades.
MS64 seems to be the most frequently-seen grade, whether the coin is Brown, Red-Brown or Red. Most certified examples are Red and Brown followed by Brown (it is not always cost-effective to have most Brown Indian Head Cents certified). Red examples are the least plentiful, but adequate quantities exist in grades MS-63 to MS-65 to satisfy collector demand. In Red, the 1883 Indian Head Cent can be found in grades all the way up to, and including, MS67.
Collectors should seek 1883 Indian Head Cents with as much original red color and bright luster as possible, and those with the fewest carbon spots. If cost is an object, look for Brown examples with smooth, glossy surfaces; they represent excellent values.