I'm back on iOS 8.4 for my iPad Air 2. The current lack of Infuse compatibility with iOS 9 is a dealkiller for me.
But that's one of the benefits of beta versions of iOS. You can downgrade easily if it doesn't suit your needs. Honestly, if Infuse worked, I'd probably be OK on iOS 9.
Just make sure you do a proper backup (and archive) of your current iOS 8.4 install before you upgrade to iOS 9 beta. If iOS 9 beta works for you then great. If it doesn't, then you can manually restore to iOS 8.4. The IPSW files for it are available. Once you've restored to 8.4 (clean restore), you can then restore your original iPad mini 8.4 setup.
As for speed on the mini 1st gen... One of the claimed benefits of iOS 9 on A5-based iPads is that it's supposed to be faster than iOS 8. That said, I heard through the grapevine that iOS 9 developer beta 1 was horribly slow on everything. I don't know about iOS 9 developer beta 3 (which is I believe the same as public beta 1) in terms of speed, but in my case it's moot because Infuse doesn't work so I'm not going to bother updating my old iPad 2 (also A5 based) right now either.
OTOH, if you're still on iOS 7 on your 1st gen mini, I'd just stay there. iOS 7 is way faster than iOS 8.4 on the 1st gen mini and iPad 2. Furthmore, once you upgrade to iOS 9 public beta 1 on a 1st gen mini, you can't downgrade back to iOS 7. The earliest version you can downgrade to is iOS 8.4