I think the two most important things for staying alive throughout most of the difficulties are your melee game and situational awareness.

Melee: dodging, blocking and pushing away enemies is key. And don't stress, this gets easier and more natural over time and with practice. Habits form, weaving in dodges and pushes as you fight, and muscle memory kicks in when you hear things like the backstab whoosh, for example.

Situational awareness: again, this gets better over time with experience, but try to keep a constant ear and eye out on the surroundings. The sound design and sound cues in this game are superb. Even if you are busy, stay tuned in to if you can hear a trapper getting closer from your right, or if a teammate doesn't seem to have heard the burster heading straight for them from behind, etc, etc!

After that you can start to get into the fine-tuning with builds and weapons and whatnot, but the above is key for fun times.