Forum Moderators: phranque
Welcome to WebmasterWorld, and congratulations on outgrowing your first server.
Moving to a new IP (I assume you will keep the domain name) used to be a big hassle, because Googlebot used to be very slow in picking up the new IP.
Several recent threads in the Google News Forum suggest that Googlebot is now doing things right, and picking up the new IP within a day or so.
The concensus seems to be: keep the old site up if you can until you see Googlebot crawling your new site.
End users will have no difficulty finding the new site.