Action-Adventure, with more Adventure than Action. Just the way I like it.
The puzzles aren't overly difficult as to distract from the narrative, but not so easy that you'll get bored between enemy encounters or cut scenes. The game's top-notch voice acting plays a big role in keeping the pace of the story moving as you're constantly in communication with your sidekicks on a com-link, and they'll chime in from time to time as you progress through the levels. If you aren't a veteran of the Tomb Raider series, I'd say this as good a place to start as any, as I had only played a portion of the original game on the PSOne prior to playing Legend, and I enjoyed the heck out of it. Take your time, go for the unlockables and achievements and this game is well worth the $30 for a new copy.