What are the most profitable quests and vending machines?

I don't vend much, so can't say about that. But for quests: Wizard, Saggi (you have to have at least 750k on hand, I think--but beware, if you go under, you won't be able to finish the quest) are my go-to quests for quick money. And after the revamp, Pete has become super awesome too!

I also have pretty decent luck for Quentin, and Cursed quests aren't too bad either (I find I get better profits with Mori but I still make an okay profit on Nori too usually). I have no idea about vending though, sorry :x I haven't been vending much lately and I never really paid attention to which was most profitable or anything even before.

I've been having amazing luck with Maleria, Cursed, and Pete quests. Wizard is also good too. If I do all these quests in a day I can make on average around 300-450k or more. Course it always depends on luck but still I find these ones are decent.

I put together a site to help figure out the payouts for each of the quests that have been reconfigured. Check out SubetaSkills

Pete, Cursed, Wizard, Saggi... they are all pretty good nowadays. You should also do Shinwa since you can get lucky and get a high-value item from her. If you're lucky you can also get mage amulets from Quentin, so there's that.

Library/Maleria are good, but they are more about the rare items you get from them. You still have to wait and hope they sell.

Cinthia just doesn't seem worth it at all.

My luck w/quests varies wildly. I agree that Sag is probably the most consistently profitable. They also frequently change or "tweak" quests, so the ones best for you may change. I'd add the item hunter to the list. Technically it's a game and not a quest, but I can usually reach levels into the 60s before I have to refuse and it resets to level one. It's good money after level 20, and better money after level 50, and so on.

As for vending, I think the question to ask is: what do you want? Each machine vends different items. Most of those items will be worth little, but you have a slim chance of getting some very valuable items. Ocean Depths is the only one that will give you Riptide, but if you're after books you should do Blue Sky, etc… I don't think they are a great way to make money unless you're looking to expand your shop inventory and can wait for prices to rise. I'd make questing and a few games my priority.