Am I able to use a controller to play the PC version of Minecraft? If so, can I just plug it in and play or do I have to do something else before being able use one?
There is no built-in controller support on the PC version of Minecraft. You will need something like Xpadder to change each controller input to a keyboard/mouse input in order to use a controller.
If you're on Linux, you may have luck with Joy2Key, found here: http://sourceforge.net/projects/joy2key/
Debian package: http://packages.debian.org/search?keywords=joy2key
Another option is QJoyPad: http://qjoypad.sourceforge.net/ which also claims mouse support.
I haven't tested these myself.