I've flown with both, Easy jet many times, and this summer Berlin - Zurich with Air Berlin. I love Easy jet they are amazing, I also found Air Berlin quite good as well. I would just book which ever is cheaper. Also both have weight limits of 20kg, but easy jet has no weight restriction on hand luggage, so as long as it fits the size and you can lift it you can carry on as much as you like.
If you go to the easy jet website, they have a tab that says to/from the airport. They will give you a link to easy bus a shuttle that easy jet runs from Stanstead to central London. You don't really have to buy the tickets in advance but it does guarentee your seat and is often cheaper if you pre pay online.