The new Ben Gurion Airport is a surprise, and it works well.

Access from the airport to Tel Aviv (and the Northern parts of the country) is easy and cheap by train (2 an hour most of the day) http://www.rail.co.il/EN/Pages/Homepa...  The station is right under the airport. To anywhere else in the country by rental car, shared taxis ("sherut") or taxis http://www.iaa.gov.il/en-US/airports/... . The fast rail line from the airport to Jerusalem will open sometime in the coming few years.

Baggage trolleys in the arrival hall and departure hall are free. All services are available: currency exchange, information, phone rentals, etc. Lots of shopping too (in the mall on the departure levels) and of course in the duty free (but only when you depart).

On leaving Israel be prepared for what might turn out to be an intensive and long interrogation process with security. The questions they ask are detailed and at times, seemingly pointless. Just answer them honestly and frankly. It is a good idea to keep receipts, brochures and other items from your stay to show during this interview.