Development, Staging and Production sites

Hi everyone, newbie here. I was able to multisite working. I only have one problem:

My customers have exisiting sites like lets say customer1.com and customer2.com

I want to migrate them, but be able to host them on my server (mydrupalserver.com) until they migrate thier hosting and site to my site.

I totally understand how to setup my box to read thier domain locally (With hosts files in windows), how would I set up a staging site so I can essentially move over thier .com

some issues I see:

files that are stored on customer.mysite.com that now should have customer1.com links....

any help appreciated.

Thanks,

Aaron