A pH of 8.4 may not be ideal, but it's not the end of the world either. That how high mine is too (Lake Michigan water is Hard and Alkaline).
While there are some fish with more specific water requirements, most of the fish seen in this hobby are able to adapt to a wide range of conditions. Research any fish you're thinking about getting to be on the safe side.
Ask your LFS what the pH and Hardness is of their water while you're getting yours tested. The larger the difference, the more slowly you will need to acclimate any fish you purchase from them.
I usually do a slow, drip acclimation with all my fish anyways, but that's me.