The easiest way is just to store it as a float/double in degrees. Positive for N and E, negative for S and W. Just remember that minutes and seconds are out of 60 (so 31 45’N is 31.75). Its easy to understand what the values are by looking at them and, where necessary, conversion to radians is trivial.
Calculations on latitudes and longitudes such as the Great Circle distance between two coordinates rely heavily on trigonometric functions, which typically use doubles. Any other format is going to rely on another implementation of sine, cosine, atan2 and square root, at a minimum. Arbitrary precision numbers (eg BigDecimal in Java) won’t work for this. Something like the int where 2^32 is spread uniformly is going to have similar issues.
The point of uniformity has come up in several comments. On this I shall simply note that the Earth, with respect to longitude, isn’t uniform. One arc-second longitude at the Arctic Circle is a shorter distance than at the Equator. Double precision floats give sub-millimetre precision anywhere on Earth. Is this not sufficient? If not, why not?
It’d also be worth noting what you want to do with that information as the types of calculations you require will have an impact on what storage format you use.