Two Gun-Using Job Ideas

[Mimilu]

That's kind of where I'm at a loss. Assuming CHM uses TP to heal rather than MP, it would make sense for it to cross class stuff off lancer (invigorate) and pugilist (mainly Internal Release and Mantra). Likewise Gunner would probably be lifting stuff from archer (Raging Strikes, Quelling Strikes) and lancer (Invigorate).

For Chemist, I would think Pugilist and Conjurer. Conjurer's Cure would be a good thing for a TP based healer, seeing as they won't have any other use for MP (so long as they used Mind for healing). Plus you would also get Protect and Stoneskin. I would think Cure, Protect, Stoneskin, Internal Release, and Matra.
For Gunner, I agree, Archer and Lancer is the best. Raging Strike, Quelling Strike, Hawkeye, Invigorate, and Blood for Blood.

[Duelle]

For Chemist, I would think Pugilist and Conjurer. Conjurer's Cure would be a good thing for a TP based healer, seeing as they won't have any other use for MP (so long as they used Mind for healing).

This is the one point of combat design in which I am at odds with the developers. The devs have chosen to go by blanket rules for the most part, whereas I'm in favor of stat scaling per class. On that note, CHM scaling off MND would mean it shares gear with SCH and WHM, and I'm not sure I like that. I figured they'd scale differently. Like DEX when you are a musketeer or have the gunner crystal equipped increases your attack power. CHM would gain healing potency from DEX and a very minor increase to attack power, for example.