If you're good at clearing dungeons, you can make multiple thousands in the first week and finish ANY possible notice board mission (though some are much more annoying than other). It's possible to clear two dungeons on day 1 if you mix-max your starting two characters.
My current preferred start is two fairies: MC starts off as Acolyte (for healing) and free NPC is fairy Apprentice with Hidden Powers.
Goblin Cave is easier than Bandit Den.
Give the Apprentice the staff and Mind Blast will one-hit-kill most non-boss enemies in a Goblin Cave, which goes a long way to cutting down damage taken.
Having one stone and one cloth (or one silk, if cloth is not available) lets you collect shards from shrines, which goes a long way to solving your sustain problems. Rock pile wants a stone, wooden statue wants cloth , metal marker wants food/grain. If you're in a pinch, store has a few of each shard for sale.
You can use shards/healing spells between fights by dragging the crystal/spell onto a wounded character.
Random treasure chests are risky until somebody has the Thief class. One mimic will easily KO an unprepared party (and on day one, you're not prepared). Might want to just avoid those until you have a Thief.