Few things for stress, it accumulate if you don't kill the last enemy in time and stress doesn't reset after an adventure so it carry over.
For supply, no need to get too much, for a short dungeon go for 8 food, 12 torch one shovel and one key and that's it.
The stuff you find around in dungeon have multiple possible outcome that can be mitigated by item. Here its your decision if you want to look up what those are on the wiki or if you want to learn it as you play, but some outcome and item needed to cancel the bad one are pretty random.
You can always run away from a dungeon, you don't lose much. If your party wipe the biggest problem is you lose all trinket
I'll put a few more tips below this, but be aware that once you figure out how to play the game it become extremely easy and repetitive, so looking at "advanced player tips" can ruin and make the game extremely boring and grindy, so proceed at your own risk.
Hero are completely expandable, you can throw them to the grinder and just grab a bunch of new one, especially now that they've severely reduce the amount of exp you need to level up, a level 5-6 hero is really nothing special.
With that in mind, here's the best way to play for early and mid game: At first just repetedly hire hero, throw that at a dungeon with no supply and equipment and just make sure they come back, don't worry too much about clearing the dungeon. Once there stress is too high, fire them all and reset, only keep the hero that randomly get good quirk and don't get and lock bad one (so locking a bad quirk like "can't meditate in town" is good cause it means there not gonne lock something like -5 Acc). At first focus on upgrading the coach so you can get more new meat and can hold more hero, you wanna get Vestal so whenever one show up hire her.
Slowly build some good hero while running and firing level 0-1, once you get 8 good hero at level 2 what you start doing is deck them out with good stuff and bring some food, shovel and key and go into medium/long dungeon (don't bring any torch you wanna do dark run). Here you don't want to clear the dungeon, the goal is to fill up your inventory with stuff to bring back (good stuff, not bandage and the like) and then once its full camp once or twice and reduce there stress as much as possible and then abandon the dungeon. By abandoning they don't level up meaning you can just rotate between two team, one goes in and clear while the other one get treated/reduce stress in town. Once those two team have good trinket and equipment/ability level the dungeon become a breeze, you can even go in without a healer for even faster run, make sure you bring some scout trinket to get the treasure room.
At that point the game become extremely repetitive and boring, but if you do clear dungeon and let the hero level up, the game punish you hard for it since a group of level 3 hero is undergear/leveled for level 3-4 dungeon. So its better to just keep accumulating trinket and leveling up the town so that once you decide to push further you have the good stuff already. This is even worse for 5-6 dungeon because your hero will level up far faster than you can accumulate gold and level the town, so you have level 5 hero with level 2-3 gear and ability level.
Overall its a fun game with solid core mechanic and art, but the execution is extremely flawed and I think they screwed up the balance. If I didn't know anything I'd say it needed another 3-6 month of development time, but I don't think that would help since there last few balance patch really didn't help. Reducing the hero exp needed to level up ironically made the game much harder which in turn made safe grindy strategy much better.
