You will need: Ammonia, Nitrite, Nitrate, PH, Alkalinity, Magnesium, Calcium test kits, a good Phosphate tester.
I use the cheap API test for ammonia, nitrite, and nitrate. For the alkalinity, magnesium, and calcium I use Salifert kits. For phosphate testing I use the Hannah Checker. For PH I use the H&M Digital PH wand [I need to get a PH probe for my RK2]. I don't much care for the wand. As well as a refractometer for testing the salinity if you don't already have one.
Others will chime in with their choice of test kits.
I would suggest a muliti-kit that has Ph, Nitrate, nitrite and ammoia for basic starters. eventually i would get individual kits that you will need like Mg, Ca, Phosate,copper...etc. once you get everything up and running.
IMO, observation is the most important thing. Any test kit will test the water, how accurate it is depends on the person doing the test. once you test, just keep the parameters stable, and you will be okay. I have come across many members here using all kinds of test kits.
I use API for everything. Don't be too concerned with the absolute values of your readings. It is more important to recognize changes...both sudden and gradual. Interpreting the colors can be challenging at times with any kit. Try to use natural daylight when comparing samples to color charts. Be consistent in how you take samples, add reagents, and make the comparisons.
When a test indicates you need to make a correction to your water, go slow, double check, see if it makes sense by observing your livestock.