I'm not sure why this isn't rated #1 for NYC attractions. Everyone should see the Met at least once in their lives. Tourists, locals, everyone. There is a suggested donation (entry fee): $25 for adults and $12 for students. Still a reasonable price for such a great place. I think most people give less.
It's so incredibly huge, it's not possible to see every exhibit/collection in one day. One of the current exhibits is photographs of the Civil War. The exhibit is much larger than I expected, but well worth the time.
It's impossible to say what is the best part of the Met. But if there is one particular part of history you enjoy, aim for that collection. You will be amazed at what you will find. I love the Armor collection, the Egyptian collection and Greek Sculpture. That alone is a full day. And you won't even leave the first floor! And the American Wing - Love it!
For the shoppers: There is a clearance shop located near/in the Egyptian collection. It's not attached to the main gift shop. Prices on jewelry, t-shirts, books and other items are drastically reduced. It's one floor below the main floor. Small staircase down, escalator up.