Interpol is spectacular. Turn on the Bright Lights is a fantastic post-punk record and a staggeringly great debut, and the proceeding records carry on that powerful sound, at least up until around The Other Side of Make Believe. As a sample, I'd recommend listening to their bonus track "Mind Over Time". It is such a phenomenal song. I quite like Paul's vocal style.
In terms of influence, I was primarily inspired by the band's visual aesthetic before anything else. (Is that obvious?) Something about the artwork for Turn on the Bright Lights really hooked me when I first saw it. I don't know. Originally, the album didn't even use Helvetica Neue for its text. That arrived with the 10th anniversary remaster in 2012: