Krupski:
The line in red..... is this necessary? And if so, what's a good delay value?
I did some experiments on this a while go. It depends on the source resistance driving the ADC input. With 10K or less source resistance, you can get away with no delay. If the source resistance is higher than 10K, then you need around 1 microsecond minimum per 10K source resistance if you want to achieve the maximum accuracy.
EDIT: I was not changing voltage reference when I did these experiments. What I was doing instead was changing the multiplexer between different input pins with very different voltages on them. The datasheet says that if you select the 1.1V reference and the brown out detector is not enabled, then the reference takes some time to start up. Also, if you have a capacitor connected between Aref and ground, this will slow down changes in voltage reference.