What DoL/DoH jobs would benefit me most as a dragoon?

Hello, after leveling Dragoon to 40 I really want to get into the other professions for a while. I am a noob to this whole crafting and gathering system so any help with info would be greatly appreciated.

What I want to accomplish:

-Master a DoL class that will make leveling the DoH class easier and more cost efficient.
-Make some Gil.
-That whatever combo I choose will be the most useful to me. [Make my own gear/meld materia into my sockets, etc.]

I plan on sticking with the 2 for the rest of my ffxiv lifetime, considering they will increase level caps so i think it is more reasonable to set my goals on mastering 2 rather than all...

TLDR: Title.

Generally speaking armorsmithing (For armors especially the high end level 50 recipes), carpentry (for spears), alchemy (potions), and both botany and mining (material gathering).