The type of sensor you are interfacing basically dictates what type of op-amp you are going to need.
pH probes are very high impedance sources that are slow to respond, when you are dealing with 500Mohm input impedance even a tiny current such as a pico amp can change your readings by a very significant amount. This is why we are looking at amps with ultra low input bias current, offset voltage can matter as well, but this can be calibrated out as long as its consistent through the measurement range and so this is also taken into account for which amp we picked out. Since the signals are relatively slow (and mainly DC) we don't care too much about slew rates and bandwidths, and is also why older op-amp designs are still quite effective today especially when cost is factored in.
When they talk about FET, JFET, LINMOS, CMOS they are referring to the physical topology and construction of the transistors which make up the op-amp. While they are all Field Effect Transistors, the methods for construction and materials used are very different and therefor yield the characteristics that we see in all the varying amps(or all ICs) out there. Each company has their own proprietary stuff too which shows up as the strange LINMOS type names, this stuff can get pretty exotic when you start getting down to this level.