I typically don't use Expeditions for hunting monsters for their materials because you'll miss out on a lot of mission rewards. Also in Expeditions, if you take to long to kill the monster they'll respawn at full health. I typically use expeditions for gathering materials like mining ore and bugs.
As for hunting monster over and over for materials it's better to farm them using Optional quests. Once you complete the Assigned quest their attached to, an Optional quest for the hunt will become available that you can repeat as many times as you want and will yield much better rewards and their always in the same spot so you get really efficient tracking them.
As for crafting/gathering tips, always keep your eye out for Flashbugs to create Flashpods(it's like a flash bang to blind enemies), Bitterbugs for making a Catalyst(main component for a TON of stuff), and Thunderbugs to make Shocktraps.
Also grab any Armor Seeds and Might Seeds for making Demon Drugs and Armor Skins. These potions increase your Attack and Defense during missions.
Never pass up on Honey. You can use these to turn your Potions into Mega Potions and you Nutrients into Mega Nutrients.
Another handy thing they added for this game is the ability to Auto Craft as you gather items. When you open your crafting menu, there is a check box next to the item. If you set it to Auto Craft as soon as you pick up a resource it will craft the item as long as you have the space. So if you have a Potion set up with Auto Craft, as soon as you pick up an Herb it will auto convert it into a Potion. Really handy ability that frees you from slogging through and manually crafting stuff you use frequently.