1) New Avengers is hit or miss, but for all intents and purposes, it was really Marvel's flagship book during the time it ran, so that's something to consider. The Secret Invasion tie-ins got tiresome, but that's way down the line. But hey, if you liked Breakout, pick up the next one and go on a case by case basis. I think "The Sentry" comes next, which is pretty decent.
2) Like Hewey said, start with Rebirth for Green Lantern and go from there. Like Brubaker on Captain America, most of what Johns has done for GL over the past 5 years has been one big, flowing story. Personally, I thought the peak was the Sinestro Corps War (which is around issues 21-25 of GL), but I'd stay start with Rebirth and go from there. It's a little tough to get into if you don't know any of the backstory (why Hal Jordan is the Spectre, for instance), but some research should clear it up and make it a satisfying read.