Which is better a push fan, a pull fan or both
I would say pull fan, as that is what most engines use.

https://en.wikipedia.org/wiki/Turbofan


  Modern turbofans have either a large single-stage fan or a smaller fan with several stages. An early configuration combined a low-pressure turbine and fan in a single rear-mounted unit.
  
  Aft-fan turbofan.
  One of the earliest turbofans was a derivative of the General Electric J79 turbojet, known as the CJ805-23, which featured an integrated aft fan/low-pressure (LP) turbine unit located in the turbojet exhaust jetpipe. Hot gas from the turbojet turbine exhaust expanded through the LP turbine, the fan blades being a radial extension of the turbine blades. This aft-fan configuration was later exploited in the General Electric GE36 UDF (propfan) demonstrator of the early 80s. One of the problems with the aft fan configuration is hot gas leakage from the LP turbine to the fan.


So perhaps fans in front can use less expensive material since they don't have to contend with hot exhause temperatures.