Capacitor Inrush Current
An NTC should work fine, as any transients will be supplied from the capacitors at a later time.    

However, here is a pretty simple soft start circuit with a small difference from those seen commonly with an RC circuit on the MOSFET gate - I added some negative feedback to the emitter of the NPN to control the rise time more predictably.
Disclaimer - I have not tested this circuit, only quickly thrown together in SPICE, hopefully I haven't missed anything stupid though. Obviously you can alter values to suit your purposes.  



EDIT - the MOSFET part number is not a recommendation (thanks Zebonaut) rather just a random SPICE part. Make sure to choose a suitable part for the circuit requirements. The NPN can be any general purpose part (like the 2N3904)

Simulation: