I remember that the critical engine is started first, no? In twins anyway.
There is no critical engine on the ground, and this has no bearing on the start order for the airplane.
The start order is sometimes varied in order to test engine-driven equipment, such as alternating engines to test hydraulic pumps, etc.
I have NEVER seen a sequence of 1, 2, 3, 4, however, as someone stated, except the 'default' Flight Sim way, but I thought we were talking "real" here.
Standard starting order for us in four engine piston and turboprop, and turbojet equipment, was 1, 2, 3, 4. Yes, we are talking "real" here. No, simulators not involved.
However, as you brought it up, in the simulator we performed the same start sequence, same as on the line. 1, 2, 3, 4.