Up above I gave you a quick guideline you can use when unsure: skip a letter. So if you start with A#, the next note has to be some form of C (not B, and not D). Then some form of E (not D, not F). Make sense? As far as I know, this trick always works, although it can lead you into situations of double flats or double sharps. Pick your poison.
I'm just now learning that a poison must be picked; I must say that I'm a tad disappointed in the math-music connection because (as I understand it) poison is not required in math
But now that I ponder this skip-a-letter-rule I somehow like it. Alphabetically speaking, it is pleasing to the eye, for what that's worth.And I don't remember if anyone above mentioned another guideline, but I really detest mixing sharps and flats in the same chord spelling. For example, you would not want to write something like C, Eb, F# (though that example also fails the 'skip a letter' test).
Once again, I like this rule too. But as you say, one rule may end up breaking the requirements of another rule.Does that help? If you get stuck, you can always throw in Mike's wildcard F.