What are the steps to moving a site to another server with no downtime or as little as possible? I will be creating its own name server also, should this be done before the move or after?
Create the nameserver and let it propagate, them move over the site and point the domain to the new nameserver, leaving the old site online for at least a week. This will avoid any downtime
Create the name servers first. Get those working. Now get your data to the new server. And then update the name server at the registrar. If you are using a database that users update, consider disabling that on the new site since you could potentially have users using the old site and the new site and the same time