Glonass
On the BAe146 the park brakes are powered by #2 engine, with electric hyd pump back up. The #3 eng provides the second hyd system power with PTU backup.
Pax load from the left and baggage & fuel on the right.
With engine start commencing after doors and stairs removed, start sequence in my co is #4, #3, #2, #1, simply because that's what every one expects.
If pax still boarding or head count still in progress but baggage doors closed, then start #4 & #3 to assist on time departure, or reduce delay, or if APU U/S, provide some aircon.
If pax on board and stairs removed, with approval of baggies, will sometimes start #1 & #2 first, to minimise delays.
If at an aerobridge, always start right first as they're furthest from the aerobridge.
It's all very fluid depending on the circumstances and I can't think of any reference that says 'thou shall start in this sequence'.