Hello, happy to hear you wish to host with us.

I would recommend signing up with Lunarpages using our sub-domain option. That would give you a URL like this:
yourname.lunarpagesowneddomain.com
That way you could get your new site ready without touching or altering your current domain or web site. Whenever your ready to move the domain over, all you'll need to do is contact
support@lunarpages.com and we can switch the sub-domain for your real domain name.
To do this type of work in the future, you might be able to do it through a sub-domain of your own domain. You would just need to be careful that the search engine robots did not crawl it, and you might put a password protection on it so only the people you want to get in can get in. Hope that helps!