Keep your left side up to date, every level which is a multiple of 5 is generally when you can go visit a crafter buddy and fill in any missing pieces.

At the start of a new dungeon, i would just quickly say "hey, first time here, let me know of anything specific to watch out for", and then pull with confidence.

I wouldn't bother with big pulls, but make sure you're not standing around forever in between pulls. Even if you're not doing big pulls, people will love you for having the confidence to start moving towards the next pull immediately after the last mob dies, or even when it's at 15%.