Honestly, if you just keep going with story and side story quests you should be completing the dungeons in a relatively painless fashion, progressively getting better as you go.

Your relic quest will provide you with a good smattering of equips and the like as well.

Don't worry too much about being undergeared as lots of overgeared players use Roulette. You have nothing to apologize for for being new, just say that you are and people should be polite and explain things.

Speaking of Roulette, you should do it daily for tomes and also to grab the equip that drops from it. That'll get you up to speed quickly. Make sure to complete all the dungeons necessary to run it though. Most are a cakewalk, but beware of Pharos/save it for last.