Is there a minimum size branch circuit for a recetacle in a hair salon? Or can the circuit be sized to the maximum expected load at a receptacle?

You would need to determine the total load on the circuit and size accordingly. The most you could hope to run on a standard outlet is 20 Amps which would give you 2400 Watts, about 2 hair dryers. A 10 AWG wire would give you 30 Amps, used with a 30 Amp outlet but is very difficult to bend and install and is a dedicated circuit usually used for a compressor or something like that. You may find it easier to install some subpanels and run to the outlets from the subpanel.