CHR is nothing but debuff resists. Skill is buff/debuff potency (if it can vary, of course: some things have fixed potency such as ballad or finale, and practically everything's potency is capped at 75 anyway) and also debuff resists.
This is, to my understanding, the opposite of how RDM debuffs work (where the MND or INT appropriately, affects the potency and resists, and the enfeebling skill only affects the resists).
Without going and publicizing all my common knowl... er, secrets, here's the general idea:
No skill or CHR, worst resists. (Duh.)
Pure skill with no CHR, pretty bad resists.
Pure CHR with no skill, moderate resists. You see this one pretty often, and it's ... okay, but ...
Balance of CHR and skill, fewest resists.
Reasonable rule of thumb is just to go with the bigger number in any given equip slot, or pick skill if there's a tie (or even if CHR wins but only slightly). That should get you a reasonable balance. There's more CHR gear than skill gear so it's kinda hard to get too much skill and too little CHR. I mocked up a theoretical pure singing/wind skill build for every available slot but body (sorry Minstrel's Coat), and still managed to get a perfectly reasonable +40 CHR on there from equipment alone. Without HQs. (Yes, it's possible to have much much more CHR if you focus purely on that. See above though, it doesn't work as well.)
Just to state the obvious, string skill does zilch when you're using a wind instrument, wind skill does zilch when you're using a string, and both do zilch if for some harebrained reason you're mainjob BRD and not using an instrument at all. (Or if you're subbing BRD, in which case the lack of instrument isn't so harebrained seeing as you *can't* use them.) So don't factor the "other" skill (whichever one you're not using) into your skill totals.