I'd say that Trouble Will Find Me is definitely the most accessible for a new listener. If you like that album (highlights are Pink Rabbits, Graceless, Humiliation, I Should Live In Salt, Don't Swallow The Cap), then I'd recommend High Violet next before listening to SWB. Boxer & Alligator are great albums but I found they took a few playthroughs at first.
Laugh Track is also a great new album by them if you enjoy TWFM.