moving old html site to wordpress

I have six domain names(websites) under one organization that will be moving to WordPress on a different host and they must remain live on old host while building new sites on new host. My question is how do I set up the new hosts domain information to build the WordPress sites and not have to point the DNS server to the new host until ready? Remember I will have six domains under one IP most likely.

Also I need to know what to put in the WordPress settings page the “WordPress Address” and “Site Address”?