I know you go through type training, base training and line training with the airline, but in what order, how long does each one take and cost?
Suggest you look here for answers to your questions: http://training.flightglobal.com/# if you haven't done already.
Gravity always wins!
The right order:
1: Type Rating.You learn everything about the aircraft and you also learn to fly it. (2 months).
2: Base trainingYour first flight with the aircraft, local flight, minimum 6 Landings (5 touch and goes + 1 full stop landing). (1 day).
3. Line training.A soon as you're type rated, you start your line training. You start flying under supervision only with instructors. (1-2 months).