For those that want to pay it, your first crew member should be either the tank or AoE mage, imo. Also, maybe restart if the 1st battle doesn't drop anything.
The cleric helps in the cave battles, but you needa do fill half the bar for departures to unlock that.
There are also some quests in the bar, that resets daily. They'll help net you wood, until you can farm caves.
-- To unlock the ship upgrade. Should try and get the 1st one ASAP, since it's more actions and crew members.
You can level up & equip your crew using the 1st button on the bottom. The third on is your warehouse; mainly used for the foodstuff to restore fatigue (hp). Not going to be useful until around 3rd island, where you'll be able to buy 5-ish items [10x3 + 20x2=50%] every 3-ish days.
Edit: If possible, you want two or more sets of crew members [mainly frontline/tanks], as the restoratives heals everyone, thus you can swap them between battles for extra fights.
The game is kinda bugged, in that the expulsion/training can be grayed after the 'characters' are done. You can reset it by closing the game.
Edit2: Added my full-ish save. Windows, so drop it in the roaming>locallow.