Since the 3DS, I've bought all my consoles at launch. So that's the 3DS, Vita, Wii U and PS4, and as long as I have the money, I'll probably get the Switch at launch too.
Before the 3DS, I didn't really have a job, so it took longer to save up, or I had to wait to get it as a present.
GameCube: I think 2 years after it came out
Wii: 2 months after launch (because of console shortages)
PS3: 1.5-2 years after launch
360: 3 years after launch, I believe