Just to add - It seems to have gone out of fashion, but at least half my punctures" are fixed without removing the wheel. If it's obvious what the cause is, then removing that by taking a section of tyre off one side of the rim and patching is no slower than removing wheel and replacing tube. Plus, you are then returned to the pre puncture position, rather than having something left to deal with at another time.
*I'm unlikely to get out again this year, so without jinxing I can say I've had three in 9,500 km, which is one more puncture than last year despite 4,000 fewer km's. I'm not saying they aren't sometimes a bit of an inconvenience, but unless there's a critical reason to avoid them (Like a commute where I had to catch a specific train) they are not important enough to influence any other decision. Modern tyres do seem to be a lot better than those of a decade or so ago, I've had several in recent years that have worn out without ever puncturing.