If you like DRG and want to try something similar but a bit different look at Monk or Ninja. If you want to try fighting from further away Bard is a good choice. If its magic you want to get a feel for Black Mage and Summoner are both strong - and Summoner has the advantage of giving you Scholar too. If you want to try healing damage more then causing it you can look into White Mage. If youd like to try leading a group rather then following one Paladin or Warrior are alright. If you have Heavensward(and have made it to Ishgard) add Dark Knight, Astrologian and Machinist to the list. You could try any of those classes next and probly do well.

And Eve is right that finishing the story is important - most of the content in the game is tied to completing parts of the story. But if you need to take a break and try something new dont worry about it. The story will be there when you get back.