The pool store that convinced me to find this place used test strips and some sort of scanner which I assume was connected to a computer.
The mentioned Taylor K1766 test is a drop test for salt only, so it's not what is usually referred to as a "test kit" around here. (It's very useful to find your approximate salt concentration, though)
A test kit, e.g the TF-100, allows you to monitor several important parameters including free chlorine (FC), combined chlorine (CC), pH and cyanuric acid (CYA).