Without making the secret to my wealth public, you'll never get rich by vendoring things. Depending on what your gil farming goal is, you have several viable options, but here is the easy one (which has already been mentioned) and the hard one (which will be vague and require you do to a good deal of research):
1) Farm shards. Some monsters drop tons of them. Bee swarms often drop 6 wind shards for me. Right now they sell for 300 gil each pretty easily on my server, and that's with zero effort. Each mob you kill like this will be worth 900 gil - 1800 gil, plus whatever other junk you find on them. If you look around, you can find some pretty dense packs of them which respawn at a very acceptable rate.
2) Farm items. I'm not talking about things that vendor for 5k / stack. I'm talking about things you can sell for 10k, 25k, 75k, 150k each. Yes, they're out there. Yes, there are some tricks to getting them. Yes, everyone can do it. If you want to be serious about this, spend some time on ffxiv.yg.com looking at items, find something that will move quickly and easily, figure out how to get it, and run wild with it. On one single item, my leveling partner and I have managed to make over 7 million gil between the two of us just grinding XP.