“Are there steel braided lines they really less likely to break and flood
my house than regular lines made of just nylon reinforced rubber?”

Steel or metal is always better than nylon, plastic or rubber.

“I ended up using soft copper tubing because I wasn't sure, but
copper wouldn't be practical for a dishwasher.”

Soft copper tubing was all everyone used to use on dishwashers for fifty years. I like to flare the ends and use flare fittings instead of compression myself. If you use soft copper for faucets you need to use a lockridge tool if you know what that is. I stopped using soft copper though because I don’t trust the Chinese quality control. Those water heater copper connectors used to last longer than the water heater until they started making them with thinner copper.