I've been given the task of migrating an Exchange server 2003 (built into Small Business Server 2003) and migrating it to a new server, which is running Small Business Server 2008.
We only want to migrate the Exchange data, not the complete SBS server.
Therefore, what would you suggest is the best and dare I say, easiest way to backup and restore this to the new server.
2003 and 2007 are two very different beasts. You will likely want to have both servers running in parallel, and migrate mailboxes through Exchange's provided toolset. Once both servers are up and running in your environment, it really is quite easy to just do a mailbox move on each user.
Here are a couple guides that seem fairly complete:
If you do not want to migrate the domain, you will not have the option to simply use the wizards to move the Exchange mailboxes.
Depending on the amount of your users the fastest way might be just to re-create the users and Exchange mailboxes in the new domain, export all users outlook folders to PST using Outlook (ExMerge might be used for automation of this process, but has the downside of being limited to 2 GB PST files so additional filters / scripting would need to ensure you do not hit this boundary) and re-import them into the new Exchange organisation.
If you have more than a handful of Exchange users, you might want to look into the powershell commands for cross-forest mailbox migration that come with Exchange 2007.
So you're not migrating the domain, meaning you're building a new domain and creating new users? If that's the case then the only real option is to export the mailboxes to pst files and import them into the new mailboxes once you've got them set up.
The first time I did this, it was from ex03 to ex07 in a shiny new domain. There was no reason to keep all the users' AD baggage from the old domain, so it was just a matter of writing the right powershell script. I'm a BIG fan of doing anything you possibly can in PS with exchange.
There's an article here, which I'd just paste in, but it's a big long-winded. But the command appears to be: