Choosing the best lobster to buy is relatively easy: You want a lively one. The livelier the better. It should flap its tail around when pulled out of the water. Dull, dreary, depressed-seeming lobsters have been in the tank a long time. Yes, they are alive, but they won't taste nearly as good as one with the energy to fight back a bit.
For the most part, you also want a lobster with a hard shell. Lobsters with softer shells have recently molted, or shed their shells, and they are likely to have more water and less meat inside - although some people swear that their meat is sweeter. Hard-shell lobsters are meatier and tend to have more tender meat once they're cooked. That said, some people like soft-shell lobsters for chowder or salad or lobster rolls because they are so much easier to get the meat out of (the softer shell doesn't require any special equipment to crack and since the meat hasn't filled out the new shell yet, the meat tends to slip right out.
Don't know how to tell a hard-shell from a soft-shell lobster? Simply squeeze the sides of the lobster's body. A soft shell will yield, a hard shell will not.
In any case, keep the lobsters alive until you cook them (you can do this by keeping them wrapped in newspaper, paper towels, or clean kitchen towels that will become nice and damp once you wrap the lobsters in them and then keep them chilled-a cooler with ice packs tends to work very well), and be sure to cook them within a day of buying them.
Also see these guide to How to Cook a Lobster and How to Eat a Lobster.
