moving to a different server

[externalaw.com]

Hi,

Just to double check

I bought a site that is hosted on shared hosting, I have access.
I own a dedicated server, and want to move this site to my server.

I do not want any downtime, or loose posts or members during the time it takes to propagate to the new servers.

I think I want to do the following. but need some help

1) backup the site as is and do a move to the new server
2) point the current site to the new database, and the new site of course also to the new database. Both old and new server therefor use the same database
3) change the DNS server names to the new server
4) after 48 hours simply delete the old server and shut the account down.

Is this the best way,

If it is.... how do I let the old server use the new servers database, as usually we set it up as LOCALHOST but I never used an alternative server before.

Thanks for the help!
(Lynn, thank you for all the other help as well, sorry I didnt post proper thanks each time!)