OK, there’s not much info on the web about this so I can confirm that yes, you can run iOS9 (9.2.1 in my case) well on an iPhone 4S. It’s not slow, it’s not weird. That wasn’t always the case with old iPhones and new OSes. For me it’s the same speed, and some of the ‘new’ features are quite nice.
I was an iOS7 holdout for a while, because it worked and I had no reason to upgrade. Then my phone began spontaneously rebooting, and taking a long time to do so. I thought maybe the battery was fried, but Apple’s online wizard says to do a full restore. I was inspired by Rob Rhinehart’s How I Simplified My Phone to rethink how I use my phone. First off, I hold onto my phones until the hardware fails for minimalist and environmental reasons, so that helps me stay simple.
Software-wise, I thought it would be good to wipe the phone, start fresh, and only install stuff I need and stop falling into the abyss of the phone (love that phrase) with social network stuff, games, news, etc.
How? Follow the official advice: backup phone (to iCloud), then do full restore while plugged into a computer using iTunes. Only my music got screwed up, but I think I can just re-sync to fix that.