OpAmp: inverting and non-inverting amplifier both amplify the signal, how to know which one to use?
There are a couple reasons (at least) for choosing a particular configuration:


If you need a high input impedance, then you are forced into a non-inverting configuration. This is commonly required in a buffering situation. An inverting configuration has an input impedance equal to the input resistor which may load the source circuit.
If you need a summing amplifier, then inverting is the way to go as the inverting input is the summing junction.



  Is it true that single supply op amp can only create non-inverting amplifier?


No. With a DC offset (on the non-inverting input) you can have an inverting configuration although the input signal will need to be ac coupled under most circumstances.