OwnCloud lives where you live. So when you move, OwnCloud is coming with you. Here are suggestions for your move.
Back up your data. No brainer because you already back it up!
Disconnect as late as possible. Your server will be down, including syncing and any calendar/contacts/notes/etc. apps you have.
Pack carefully. Hard drives and laptops can break if jarred enough.
Power off properly. Your OwnCloud server is rarely off, so make sure you disconnect connections to your hard drives and shut off your PC.
Reconnect as soon as possible. Find a place in your new home that is dry and cool. Make sure you have a ethernet connection to your router.
Update your DNS to point to your new home. Go to whatismyipaddress.com, find your new IP address, and update the DNS for your domain. You might
Forward your router ports. HTTP is 80, HTTPS is 443, SSH is 22, FTP is 22. Do this on your router.
Remount your hard drives. See Owncloud and an external hard drive.
Start apache server. It should start on its own, but run your server startup.
sudo service apache2 restart
Update your server configurations. If you are using a domain name, then there is much less changing. If you are using IP addresses (Do not do that!! Do this Domain Name for your Home Computer!!), then modify these to start:
Enjoy your new home and still working OwnCloud!