What is the "correct" setup for domains in a multisite network

I have an existing subdomain multisite network, let’s call it network.com. I have about 9 blogs on this network, and currently use the MU Domain Mapping plugin and am thinking of switching to the WPMU DEV Domain Mapping version.

My question is this: When I’m logged into my individual blog’s dashboard, what should the URL be? Right now on mine it’s blogname.network.com, but the front end is blogname.com.

I think this is confusing Jetpack and possibly other plugins. I had to re-connect my site to WordPress.com and found that all my stats were gone. I then edited the site URL to say blogname.com from Network Admin and it re-connected to WordPress.com properly, but that broke my media URLs (blogname.network.com/files/yyyy/mm/file.jpg).

So I’m pretty confused myself! If someone could let me know if what I’m doing is correct that would be much appreciated. And also, if you can tell me how the WPMU DEV plugin is better than the existing one I’m using that would be great as well.