I have an iPad 2, and its has been fine on iOS8, it is on 8.4 now and is running fine.
Do not really see any Safari problems (not that I use it often), as I use the iCab browser all the time and that runs very well on the iPad2.
Really is worth clearing your safari cache now and again, Settings -> Safari -> Clear History and website Data.
Also if you use any newsstand apps, they often have a manual cache clear from within the app, that does build up.
But a restore to factory settings may help you and as long as you do a backup to iCloud it will bring all your settings and apps back after the restore.
Have been part of the iOS9 public beta and the iPad2 works well on there too. Seemed quicker in some respects, mainly the animations. Saw no problems, apart from a few apps were not compatible, but sure they will be on official release.