For ammonia, nitrite, nitrate and ph. The api ones are fine. You normally use these while cycling. They are inexpensive and give a somewhat accurate reading. I found the nitrite hard to read between 3-5ppm. After your cycle is done it's nice to test every now and then just to get a piece of mind.
Theory is, if the bacteria is healthy it will always read 0.00 ammonia, 0.00 nitrite and like 0.5 nitrate. So no point I really testing for them anymore. But like I said, for a piece of mind.
Other params like calcium, alkalinity and phosphate are the big ones you really need to know as they effect the effect the growth of corals in your tank. For these I bought and advise the hanna checkers. Pricy, yes but accurate and digital. No more trying to figure out what shade of blue this is.
Hope this helps