A couple more simple tips:
Once you unlock expeditions, you can use them to level up the higher rarity monsters you can't have in your party yet. Worth it to get a head start on levelling good finds.
Once you have a quropeco, a good way to get cash and large monster drops quickly is to accept all large monster subquests for the area, walk outside town and start summoning. Do two or three then go back in, turn in the quests, re-accept them and go back out. If you've accepted the forge quests for the equipment you want to make, it'll even flag up relevant drops in blue after each fight, and tell you when you have the items you need. You're on your own for upgrades though, but like the main series games it's worth having half a dozen weapons you're working on as you never know what will turn up.