I do alot of cooling and refrigeration work and would be happy to help but I'm nto sure I understand your question: If you've got the condenser fan and compressor right, the rest is just typically the thermostat and the safety controls (high pressure cut out, low pressure cut out, etc) all wired in series with the thermostat to prove everything is working properly.
If any of the safety controls is open (meaning there's a problem) than the compressor and condenser fan contactors don't get energized.
But some systems (here in the US) use 24V for control wiring, some use 120V or 208V. There are also all sorts of controls. If the evaporator coil is directly submerged, you may want to prove the circulating pump is pumping or prove the evap temp so you avoid freez-ups.
If you're in an area that gets cold, your condenser fan may need to cycle on and off with a condenser pressure switch instead of running all the time. (known as a low ambient control)
Most of the time, condenser fans and compressors are energized through contactoras who's coils are energized by the t-stat and 24V transformer with all the safety switches in series with the thermnostat/transformer/contactor coil circuit.
