Moving and mapping existing sites to MU

I just got multisite set up, and will be using subfolders. I have 6 existing Wordpress sites that I want to move to it, and then map their existing domain names.

Should I set up a new site, which would be mainsite.com/site1, then move the files to it, then change the name servers, and then map the domain name?

I hope it can be done that way, so that I can make sure the files and database get transferred successfully before I have to shut the existing site down.

Also, should I name the subfolder site something more like the real domain name, rather than site1?

Thanks for any advice!