A great starting point for Green Lantern is definitely Green Lantern: Rebirth by Geoff Johns. It revitalizes Hal Jordan's character and is incredibly accessible for new readers. It lays the groundwork for the modern Green Lantern mythos and introduces key elements of the universe, including the emotional spectrum.
If you're looking for more depth, Blackest Night follows up on that and is a massive event that changes the landscape of the Green Lantern Corps. The way it thoughtfully weaves in horror elements with superheroics is really compelling, and you can feel the influence of the animated series in its character portrayals.
If you want something to read while you wait for the new series launching later this month, I'd recommend starting with Emerald Dawn, which gives a solid origin story for Hal as well. Have you seen any of the DC animated features? I find they capture the essence of these characters really well!
