What is necessary for mathematics graduate school?
It's hard to say.  Your background sounds strong.  Your interests are more to the applied side of pure or the pure side of applied.  Really, a bit more towards applied than pure from my impression (e.g. CS interest).  

I don't think you could go wrong taking another stats class (applied or theoretical, time series, whatever) or an operations research class.  (Not on your list, but a guess.)

If you restrict to choosing from the list, consider number theory.  Kind of useless but a lot of fun. Don't grind something you don't like just to look good.  I would pass on the second semester of theoretical calculus.