With winter on the way, the bike will likely spend a good chunk of time in the garage, so I've figured I might use the downtime to refinish my wheels, as they're white, chipping, and in general disrepair. I've looked into a few options, but working out of my garage pretty much limits me to spray paints and plasti-dip.

I've never painted a motorcycle wheel before, is it necessary to remove the wheel bearings or can I get away with covering them with newspaper or something similar? Any recommend brands if I do go for a paint? Something strong that will resist chipping and be easy to clean.

You can cover the bearings.

As for how to do it....

Look at Eastwood.com.  They have wheel paints and everything to prep it properly.
One cool item they have is a cone - like a doggie head cone - you can put on the wheel so you can paint it without removing the tire.

PS: Diplicolor also makes good wheel paints

If you decide on a flat-finish type paint, take a look at plastidip. Applied properly it looks like a textured flat finish, easy to remove, but durable enough to do duty as a wheel paint.