I am gonna sell my Xbox 360 elite tomorrow and buy that new Xbox 360, but I remembered people telling me about transferring data, could I not simply recover my xbox live gamertag, and have all my stuff, like friends, map pack downloads, and achievement scores?

You can purchase the Xbox 360 hard drive transfer kit, from a place like Amazon. Or, if you have a large flash drive, plug it into the old xbox, copy the data onto it, and then plug into the new one. You will keep your achievements anyway, as that is associated with your gamertag.