To avoid damage...is it plug the cord into your cell phone first and then into the wall (?) Or: Plug it into the wall and then plug the cord into your cell phone (??)

Technically it doesn't matter. Your phones are called smart phones for a reason.

I'm not sure it makes a difference,  but I put the plug in the wall first, and then plug the phone in.

I've change most of my outlets over to accept USB plugs. I can plug my phone in almost anywhere in my house to charge it. No need for the charging cube.