Normal climate control A/C operation

[nice1guv]

I have a 2004 update model diesel with climate control, and was just wondering what the normal operation is for the A/C.
Mines seems to vary the time it takes for the A/C to kick in.

You turn on the climate control with the fan on low (lets say 3 bars),
the temp is set at the minimum (16C for me, ~60F for US?),
the air is towards your face (although it doesn't matter where it goes),
set to re-circulate,
outside temp is 25C, 77F,
Press the A/C button.

How long does the A/C actually take to kick in?
Is it instantly when you press the button, or does it take a few minutes?

I've started the car from cold and it has kicked in instantly, but usually it takes a few mins of driving before it starts.
When the car is hot, it still generally takes a few mins of driving as well.
If you stopped the car for a short while and then restarted, the A/C starts straight away.

Once it is going, it is freezing cold and will run continuously for however long it is on for.

Is this normal A/C operation?