Suppose I want to put a cubesat in Titan's orbit (saturn's moon). and I want to calculate what rocket power I need, how do I calculate it? Where do I begin? total mass of the probe or delta-v needed? I need to know even the costs, so I need to know the strength and distribution of the engines, how is it calculated?
You will need to know the impulse you will need.
To derive this, you need to know the mass of your probe, and the required delta-v.
To know the delta-v you need to know the route you're going to take.
Your route will also guide you as to the required thrust to weight ratio you will need at the different points of your flight, which will inform your decision about the type of engines to use and the typical mass fractions.
Then you work backwards calculating the minimum impulse required of the stage, from the weight of the payload and required delta-v for the stage then finding the vehicle that will provide that.
This gives you the payload weight for the stage before it, and you know the delta-v required from that, so that tells you the minimum impulse required for the stage.
That probably gives you the weight your 2 or 3 stage launch vehicle will need to put onto an escape trajectory, which lets you choose a launch vehicle.
The fun bit is deciding how much delta-v gets assigned to which stage, particularly the launch vehicle.