This is plant specific.
Maybe you live in India and your permit only has that TSS has to be below 1000 ppm before discharge.
Maybe you live in Brazil and your permit says your TSS has to be below 200 ppm and phosphorus below 100 ppm.
Maybe you live in Norway and your will have to monitor 10 parameters all with rigid guidelines.
Perhaps the plant's influent is very good except with one high parameter such as ammonia, in that case if all the influent's parameters already pass the legislation for discharging then the only parameter that will be important is going to be ammonia.
Remember that unless it is a municipal wastewater plant, all wastewater plants are in the business cleaning the process for something that was made and ultimately the goal is to turnout a profit, this is why the only parameters that are important are those in the permit to operate the plant and the ones in the regional/federal legislation. Company image is also important but as an operator you're looking at paper and lab results when it comes to parameters.
I found this picture which can be useful as many parameters have to be monitored daily, in addition to the final goal parameter's which I described above.