It depends on where you want your audio to hit the emulated mixer and the type of flow you are attempting to emulate. In an analog studio the audio hits the mixing desk preamp or external preamp first then is recorded to the tape machine. from there it leaves the tape machine and goes back to the mixing board. From there began the compression and eq inserts. The channel is then bussed and the busses are then all summed to the master fader and finally back out to the two-track tape machine.
So for simplicity you could run tape emulator first then console emulator, eq, compression, send to group/bus fader w/ bus console emulator, send to master fader w/ buss console emulator, buss compression/eq, limiter, tape emulator.
Also if you are recording a guitar and using software guitar amp, place that first because in the real world that happens before hitting the console/tape.
On the other hand if you imagine you are emulating initiating playback from a digital box to a console, or from the compiter to a mixing console and you are more interested in summing fx not real world signal flow, placing the console emulator at the end of every pro channel chain is ideal.
Other than those two scenarios just put it where it sounds best and enhances the track the way you want it to.