Hey,
Thank you everyone for your immediate interest in helping resolve my issues.
I am running iTunes 12.1.3.6 (obtained this info from iTunes --> About iTunes), 64-bit. My machine is also 64-bit, running Windows Vista Home Premium.
I did not mean to imply anything when I said 12.1.3 was "pushed" to me, other than that I received the upgrade prompt, likely along with a QuickTime update as they seem to appear in pairs, some time ago, and willingly chose to install it.
The real issue is with iTunes rather than the iPad (which is running iOS 9.1), as iTunes also crashes with no devices connected. It doesn't seem to necessarily be triggered by any actions either: While upgrading any apps causes a crash, just a moment ago I merely clicked over to the apps page, away from music, and that also prompted a crash.