RaceEngineer:
My question is rather: if I buy an Arduino, is it like connecting some wires and programming the right software? Or do I have to add components to the PCB and build it myself?
FIRST - An Arduino board comes ready made but a lot depends on how robust and permanent you want your finished system to be.
With an Uno or Mega you can make connections by plugging wires into the sockets - which is great for prototyping. But it may not be reliable in the longer term as vibration, dust or moisture could degrade things. Soldered connections or screw terminals are much more secure. It may make sense to use an Uno or Mega during the prototyping phase and then change to another board for a permanent project. This can usually be done with little or no change to the software.
An Uno is probably the best board to start with because most software and add-ons work with it.
SECOND - it is possible that your sensors or output devices are not directly compatible with an Arduino and will need some components between them and the Arduino. An obvious example would be a stepper motor driver - an Arduino cannot itself manage the high currents needed by motors.
...R