We know that the gain is R2/R1, and we already know what level of gain we want, for example if we want gain of -1, then R2/R1 = 1
But what about the absolute value of R1 and R2? No matter whether I choose R1 = R2 = 1Meg or R1 = R2 = 1Ohm, the gain is still -1. What are the considerations involves in choosing the absolute value?
Super Low Value
If your choice is around this region, then something is really wrong. For example if your input is 1V, and you are expecting 1V at output of the amp with resistance of 1Ohm, then you are demanding that both the signal source and amp gives out 1 Ampere, now that is too much to ask for. Typical application only requires current level up to 100uA.
These are the values for some high bandwidth operation – when you need to amplify MHz range of signal. Essentially your amp and resistor will be quite hot during this operation. But such is life, speed does not comes in cheap
When your opamp gets hot, input current and offset voltage drift, which can readily cause your accuracy to suffer.
These are the typical values for typical operation, speed of operation are about 10kHz 100kHz typically.
These are the typical values when the application used battery, it will be slow (few ms), if your amplifier is of high speed type, then you might want to consider adding 10-20pF across R2 for stability sake. The capacitance can be calculated, it is not black magic, we will go through this subject one of these day.
Also, as the resistance value increases, the input bias, offset current of opamp will increase, as 100pA * 1MegOhm = 0.1mV of error, which can be an issue if your circuit accuracy is critical.