In the end, I liked the larger size of the iPhone 6 better, so that's what I now have to replace my three year old 4s.
The transition from the 4s to the 6 was actually pretty easy. I normally back up to the cloud only, but in preparation to switch to the new phone, I synced with iTunes, downloaded all of my purchases and then did a full backup to my computer. Then I unplugged the 4s, plugged in the 6, and restored it from the backup.
To my amazement, it worked and all of my apps, data, etc. were loaded flawlessly. I had to enter passwords on a couple of apps the first time that I used them (like my gmail), but other than that I didn't have to do any other setup.
My son is now using the 4s as an iPod essentially, since it does everything but make calls as long as it's connected to wifi. In order to get the iMessage (text) function to work, I restored it to factory settings, then set it up as a new device using his apple ID. Then we synced it using iTunes to get all of the apps he wanted (he's already got other apple devices).
It was a surprisingly pain-free transition, so I was very happy with it. So far I'm also very happy with the phone itself. It is much slimmer and larger than my 4s, so it feels very different in my hand. The screen gives me a really beautiful image, very crisp and bright. The battery life is ok so far and it's pretty comparable to when my 4s was new. Of course I've been using it a lot more than normal, so we'll see how it does over the next few months.
Now that I've successfully done this transition, I'll know exactly what to do to prepare for my son's first fully functional phone in the future. At some point he'll get a phone, so at least I know I can backup what he's got on the 4s and restore it to a new device (I'm assuming he'll get an apple since he loves mine so much).