If they add Mechanic/Machinist I hope they don't do it PUP-style. I've heard some talk about magitek armor and if anything I think that could be used to make something new, but with some of the PUP spirit in there as well. You could build different magitech armor/equip them differently depending on what you are fighting. As it is magitech, you should have it on you/sit in them. If you have seen Full Metal Alchemist, something like what is used there to replace limbs could be used, or the full blown mech armor you hop into. Or both.
I don't know at all what they have in mind for magitech armor(Or if it will even be in game, since when i saw it mentioned it seemed to be something that they are thinking of using for something, but not sure yet), and usually I'm not a mech-fan so to speak, but looking at FFXIV I think it could fit well into the world. FFXIV society seems a bit more advanced when it comes to technical advancements than a pure old-school fantasy or horses, swords and boards world. I think they should utilize that to their advantage and make something different/unique.
Chocobo Knight would be fun, doubt we will see it, but can always hope.
Gun wielder, yes please.
More DoM. There are 5 DoW, and I am not saying the classes have to be equally spread out over the different types, but two magic classes is too few for me.
Support classes in general.
Chemist would be cool, but I don't see it being implemented as part of the Alchemist class(Not at release anyway). Simply because, it seems the crafter classes are not supposed to be very good in combat. Yes they can throw a stone here and there, and I dunno about you, but if they add Chemist as a class, I want to be more useful in combat than that. Now, if they decide to add abilities to all crafter classes and make them more viable combatants, then making Alchemist the Chemist is fine, but it has to be for all crafting classes then and like I said, the way it looks now that is not something that fits into what we have heard about crafters and their combat viability yet.
Of course, maybe SE has something up their sleave and will make the crafter classes the support classes of the game as well, and I guess that could work, but personally I'd prefer a more dynamic approach to Chemist, with a mix of support/debuff/damage(maybe less damage?) making it an entirely new class instead. I think having Chemist as its own class would give it more room to be and/or evolve into a fun unique class, than as a part of a crafter class.
Overall I guess I would just like to see more adventurous classes than what we have seen so far. Apart from crafters having a bit of a different role than in most other games, they seem to be taking the safe route with almost all of the classes, I would like to see some more uniqueness. Then again, I guess that is something for expansions. It is, after all, better to make sure most people are happy and have something they enjoy to play, which they are doing when deciding to go with the "safer class options". The rest can always be added later.