I highly recommend heating the bed first.
Lets look at two examples on typical 3D printer. Let's say it take 2 min for the hot end to heat up, and 6 for the bed to reach temp. If you have the power, obviously you would heat both at the same time and be printing in 6 minutes .
--Hot End first.
Hot end reaches set-point in 2 minutes, then the bed warms up in 6 minutes. The hot ends heater is idling for 6 min, allowing for the heat to creep up the heat-break, the plastic to "toast" in the melt zone, nozzle and more.
Bed takes 6 minutes to heat up, followed by 2 minutes for the hot end. The bed has been idling for 8 minutes, has fully soaked up the head to a uniform temperature, and just as the hot ends melt chamber reaches temperature, the printing has starts.
Both headers must idle at a much lower power than what is needed for full warm up. Either way has the first heater at idle, not pulling it's full power and allowing the second heater to do so. The loads are actually much different, with the Bed first actually pulling less total power than the Heater first (I have the fuses to prove it on my Rostock Max.)
For those reading this, wondering how it can be changes, it's done typically in the slicers "startup gcode" by calling in the correct order M190 and M109 and not using M140 and M104.
M104 = Change Hot End set-point and continue.
M109 = Set and Wait for Hot End to reach new set point.
M140 = Change Bed set-point and continue.
M190 = Set Bed temp and wait until at set point.
Cura heats the bed first by default and I don't think it's changeable. It happens in gcode that is inserted before the "startup gcode".
Slic3r will do it either way, as it's done all in the startup gcode.
Now if you are messing with the start/end gcode, be sure to use M140 and M104 to shut down both the heaters. Don't hang your print run by having the printer sit waiting for the heaters to reach 0 C.... which they won't.
(I think that the temperature of 0 is a special case, and it's just shutdown, but I haven't tested. I think the heater and bed Minumum temperatures come into affect. )
PS: I could be wrong, but this is what I found on other printers.