There are a few techniques here that just make life easier and a procedure or two that will keep the electrons happy.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
[Airplane Flight Manual §02-06-20]
One of the questions I get on a repeating basis about GV series airplanes is why we bother placing the PTU switch to NOT ARMED prior to engine shut down if we plan on starting again with the before starting engines thru flight checklist. Why not just leave it ARMED? I believe the reason is to save on an unnecesary spool up on the PTU motor. If you go to NOT ARMED, the motor remains idle until you start the right engine again with the left engine not running. If you leave it in ARMED, the PTU motor spools up once you shut down the left engine and then spools down as the right engine winds down. When you start again you get a second spool up. So do it the way the checklist calls for. Maybe you'll prolong your PTU's life a couple of days, eh?
NOTE: With the APU GEN ON, pausing two (2) seconds between selecting each FUEL CONTROL switch OFF will prevent a possible electrical break-power transfer.
A good way to build in your two seconds here and get things done is to shut off the left fuel control, then turn off the nose wheel steering, then the right fuel control followed by the beacon.
CAUTION: ENSURE THAT THE APU AIR / ENGINE BLEED AIR IS OFF AND CABIN IS FULLY DEPRESSURIZED PRIOR TO OPENING MAIN ENTRANCE DOOR. ENSURE THAT THE AREA UNDER THE DOOR IS CLEAR OF OBSTACLES AND PERSONNEL PRIOR TO OPENING THE MAIN ENTRANCE DOOR.
CAUTION: THE MAIN DOOR CAN ONLY BE OPENED WHEN THE PRIMARY AND SECONDARY LOCKS ARE PROPERLY SEQUENCED. ENSURE THAT THE AUX PUMP IS NOT RUNNING PRIOR TO OPENING THE DOOR. IF THE DOOR DOES NOT OPEN READILY, CLOSE THE DOOR AND RE-INITIATE THE DOOR OPENING SEQUENCE.
Make sure you have extracted all the information you need from the MCDUs and CMC first.
Make sure you or the crew have completed all cabin chores first. If you need to complete a G450 Normal Procedures & Techniques / Water System Purge, you will need to wait on this step.
Turning the APU bleed off really doesn't matter but you really need to be vigilant about turning the engine bleeds off. See G450 Systems / APU Load Control Valve Logic for an explanation on why this is critical.
Before you shut down the APU, make sure the wheels are chocked and release the parking brake. You should do this first because there is no guarantee how long the brake accumulator will hold those brakes so you want the APU running until you've done this. See G450 Systems / Landing Gear Wheels and Brakes for more on this.
You may also want to pull up the GND SVC synoptics before you shut down the APU to get an indication of your engine oil levels. See G450 Normal Procedures & Techniques / Post Flight Servicing for more on this.
You may also want to check your APU run time now since that information on the CMC is not available without AC power.
You may need to move the yoke and rudder pedals to center to ensure the gust lock is engaged. If you skip this step the engage point can become worn and eventually will not work.
CAUTION: CHECK ENGINE OIL QUANTITY BETWEEN 5 AND 30 MINUTES AFTER SHUTDOWN. DO NOT SERVICE OIL ON A COLD ENGINE. IF IN DOUBT, RUN THE ENGINE AT IDLE FOR 10 MINUTES. RECHECK OIL LEVEL TO DETERMINE IF THE ENGINE NEEDS OIL SERVICE. FAILURE TO FOLLOW THESE PROCEDURES COULD LEAD TO DAMAGE TO THE OIL PUMP.
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Gulfstream G450 Airplane Flight Manual, Revision 35, April 18, 2013
Gulfstream G450 Quick Reference Handbook, GAC-AC-G450-OPS-0003, Revision 34, 18 April 2013