You need to do this right and that is to treat all the water as it exits your pressure tank.
What type of equipment you use depends on what and how much of it is in the water like, hardness, iron, manganese, any H2S etc.. So you need a current test for those things, minus the H2S if there is no odor to the water, and then you can post the results and go from there.
Nitrates and nitrites should be tested also.
You could shock the well too but then if a test shows no Coliform, I would never trust it to not have bacteria contamination at least from time to time. Bacteria and nitrates an nitrites come and go increase and decrease from time to time due to precipitation.