Does Apple have a preferred method for charging the ipad via a wall outlet? Should the unit be turned off, in sleep mode, or can charging occur while on and in use? I'm assuming all three modes are acceptable but is one preferred?

Apple says you can charge either in sleep mode or turned off...the fastest charging will occur when shut off as no resources are being used. Charging can also occur while on and in use but will be a slower rate depending on the load on the system.

As Ralph explained, it really doesn't matter.

I'm not sure that this particular behavior still occurs, but it used to be that if you turned the iPad off, plugged it in to recharge - and the battery is at a certain level, the iPad will start up anyway on its own. So if you see that happen - it is normal.

I'm not sure if that still happens with the latest updates but that would happen to me on my iPad 3 if I powered the device off.