Short answer: Darkest Dungeon heroes are disposable, and the game is designed around you constantly swapping, losing, and gaining new heroes as stress and negative quirks take their toll on them. So a full party wipe or losing teams of otherwise good heroes to stress isn't unheard of and you shouldn't feel too bad about it.
That said, there are strategies to bring your characters back from sanity loss. The Jester is the strongest stress-relieving character, and having one or two of them on a party can get the party through a dungeon without any significant lingering stress so long as you have characters that can do good damage. And if you get a good handle on which enemies are dangerous and which enemies cause high stress damage, you can learn to artificially keep the enemy alive and recover more stress than it deals to you. I asked a question here that might be helpful if you want to go that route.
So, one solid strategy you could use:
1.) Grab four heroes off the stagecoach, making sure at least one of them is a Jester, also keep an eye out for Crusader and Houndmaster, who can do good damage and also reduce stress, and the Vestal, who can recover health.
2.) Buy the Jester Inspiring Tune, and whatever other stress/health healing moves you can get for the other members.
3.) Go into an early dungeon with the intention of getting as much money as you can without getting too roughed up.
4.) Fight enemies and make absolutely sure you keep your sanity in check by spamming Inspiring Tune at every opportunity when fighting weak enemies and removing sanity-affecting enemies.
5.) Use the money you earn in the dungeon to pay for Abbey/Tavern visits for your extremely stressed party members that didn't go in that day.
Then repeat that with the slightly stronger and (hopefully) unstressed party members. And the system gets easier as you unlock more armor and weapons.