That's a good point, for some reason I was thinking my mini 2 came out with 6. It's probably fine to go to 8.4, I've just heard so many mixed reviews of it that I'm still wary when 7.1.2 works fine. From what I've read 8 seems kinda mediocre, especially compared to the positive things I've read about 9's beta. On the other hand I have 8.4 on my iphone 6 and have had no problems, so I may just be too cautious.
You aren't being too cautious, you're being smart. My iPad mini 2 was having issues even on iOS 7.1.2, same issues OP mentioned.
I was hoping iOS 8 would sort of help my iPad mini 2, as simple things stuttered on iOS 7 like rotating the keyboard, rotating the App Store, starting Siri, using control center over keyboard, over an open folder, or over the lock screen, etc... But no. iOS 8 made everything worse, and added new performance issues. I was appalled. My iPad lags and stutters from just exiting an app I've been using for awhile, as well as simply tapping the address bar in safari. Spotlight search comes down at a lower that 60fps framerate because of the blurring effect, and sending messages always stutters unless the conversation is completely empty. There are more problems but those are my prime examples. I would leave my iPad on iOS 7 if I were you.
iOS 9 is very similar to iOS 8 so far, except a couple things are fixed/alleviated! Sliding down spotlight is a bit smoother, and the keyboard comes up a bit smoother as well. Tapping the address bar in safari is somewhat smoother because they made the blurred favorites screen wait longer before popping up (keyboard comes up smooth at first but stutters at the very end when the favorites pop up). Control center is now smooth on the lock screen because they made it so the "Slide to Unlock" text disappears when you slide up. Navigating away from an app with a multitasking gesture while the keyboard is up no longer stuttery, and Siri doesn't look so stuttery as it is initiated (although it still does stutter some) because the content doesn't move backward as it is blurred like in iOS 7/8. HOWEVER. The app switcher is a total and complete mess. On my iPad mini 2, as long as there are 3-4 apps or more in the switcher, entering or exiting apps is carried out at less than ~30fps. Scrolling lags too, mostly around the home screen "card" in the switcher.
All in all, iOS 9 is better in some places, the same most everywhere else, and in a couple places worse than iOS 8 in terms of performance. This is actually exciting to me because we still have 1-2 betas to go, and things already are fairly good. The only main issue is the app switcher for me. I think that just needs polishing because even on "Increase Contrast", entering and exiting apps stutters.