There are a few general criteria that influence probe design:
How far from the Sun will the probe operate? This dictates:
- thermal design
- radio design
- launcher size
Anything out to Jupiter can be powered by solar panels, go further out and you'll need an RTG. Depending on this distance you may also need heaters to keep the interior of the spacecraft warm enough to function. Or if you go to the inner solar system, you need to think about removing excess heat.
The further away you go, the better your radio needs to be. This drives e.g. amplifier size, antenna size, receiver quality.
A probe that orbits Jupiter or Saturn needs more radiation hardening than one that's destined for Mars or Pluto.
To get further out, you need a bigger launcher (and even then you may need gravity assists). The size of your launcher determines the maximum weight of your probe, which in turn drives all other aspects of the design.
The instruments are driven by the mission (what science do we want to do?) but are constrained by power, weight etc.
So, what do you really need?
- A radio,
- Enough power to run 1. and 2., so solar panels or an RTG,
- (usually) some maneuvering capability, so thrusters and/or reaction wheels,
- A chassis that holds all of these.