As folks have said, it depends on the instructor. Those I've met in the UK "who know" seem consistently to say "standby before changing". So do the ATCOs.
I'd like to hear the view of some US ATCOs, because over there I got my knuckles rapped for selecting standby first!
I don't know whether TCAS causes the transponder light to flash - does anyone? From the rate mine was flashing at Bourn this week, there were a lot of interrogators in the vicinity. Can't have been ground-based SSR, so I concluded it must have been stuff up above.
But I have been known to be wrong
Where is 2Donkeys when you need him?