The simple answer is no! There are recommendations but there is only one rule you must adhere to....if it sounds good then it's ok & it doesn't matter how you got there!
Some people like to EQ destructively first; removing unwanted frequencies, then compress, then EQ again to boost the frequencies you like but this is only a starting point. As you get used to techniques & equipment, you will get to a point where you will hear something instinctively know what compression or EQ it needs.
I find it helps to sort my thoughts into either "corrective" or "creative", keeping corrective effects on the channel strip & creative things like delays etc on aux sends but that's just me. The only real rule I have is self imposed, I never use reverb on bass it just makes it muddy & sound awful!
I hope this helps!