Taxiing with one engine: Is engine #1 always used or do they switch?
Airbus aircraft have 3 hydraulic systems (Green, Blue, Yellow). Green is pressurized by left engine, Yellow by right engine, and each one can be pressurized by the other using the PTU. In addition the Yellow circuit has an electric pump.

The Blue circuit is a backup pressurized on demand by several means (electric pump and RAT).

Each circuit powers different aircraft components:


Source: A320 FCOM

The choice of which engine(s) to use is based on the need to have pressure:


For brakes
For nose wheel steering system.


Normal brakes and nose wheel steering are pressurized by the Green system. The brake accumulator must be pressurized, this can be done by running the an electric pump without starting an engine..

Engines are numbered 1 for left, 2 for right on twin-engined aircraft and from left to right (1/2 and then 3/4) for four-engined aircraft.

From this document:

Which Engine to Use?


  A320 Family: ENG 1
  A330: ENG 1
  A340: Outer engines (ENG 1 + 4)  


Why?

A320 Family:


  
  ENG 1 pressurizes GREEN HYD (NWS + NORM BRAKE)  
  YELLOW HYD pressurized via ELEC PUMP  
  PTU is not needed  
  


A330:


  
  ENG 1 pressurizes GREEN + BLUE HYD  
  HYD BLUE ensures ACCU PRESS  
  ELEC PUMP are not needed  
  


A340 (outer engines when possible -- exception would be a narrow taxiway and FOD risk):


  
  ENG 1 + 4 pressurize GREEN HYD (NWS + NORM BRAKE)  
  Check ACCU PRESS normal before ENG start  
  ELEC PUMP are not needed