Wow. Just wow. I played and enjoyed the first two Bioshock games, but always felt they recieved a bit more credit than they deserved. Bioshock Infinite makes the previous games feel like prototypes; this is a true marvel in game design and storytelling.
The combat may not be groundbreaking (you now have a regenerating shield ala Halo), but it's brutal, every weapon and tonic in the game is varied and useful, and for the first time in the series it's just plain fun. That doesn't mean it's now a mindless shooter; the multi-layered, biting, emotional narrative makes just about every other video game plot look like amateur hour. The highlight is Elizabeth, one of the best written and useful companions to ever grace a game; she'll toss you ammo and health in the middle of a fight, open tears to another dimension to turn the odds in your favor, pick locks for you, never needs babysitting, and quips, "Oh my god!" when you grind your skyhook into some poor sap's face. She's awesome.
I won't get into plot specifics, partially to avoid spoilers (the less you know going in the better), and partially because I couldn't even begin to do it justice without breaking the game down scene by scene and analizing every visual cue and line of dialogue, and I'd probably need a degree in quantum physics. It can be enjoyed and absorbed on a multitude of levels, from a simple father/daughter parable to the dark history of The United States to the folly of Patriotism and Absolutism, and a whole lot beyond and between. I really cannot reccommend this enough; it's so finely crafted and carries so much weight I'd tell anyone who doesn't even like games in general to buckle in and experience something special. It's just so good.
*Quick note about the DLC: long story short it's not that good. I played the arena stuff when it first came out and was nothing special. Burial at Sea is a two part story that ties Columbia and Rapture together, but really it just dilutes and over-complicates what really didn't need explaination. The first part returns to the well of Rapture and it's pretty standard, but ends right when it gets going. The second part has you playing as Elizabeth, which going by the main story should be amazing... but it's not. It's poorly done stealth with no other options, and quite frankly it's boring. Unless you get it in a bundle for dirt cheap, just don't bother. Even then it might not even be worth the time and the bad taste it leaves in your mouth after the mindblowing main game.