Hi

im looking into moving from Exchange 2003 to Exchange Online. What would be the recommended upgrade path?

I want to use single-sign-on and migrate the mailboxes from the old server with as little downtime as possible. 

With Exchange 2003 you will use Cutover Migration, or Staged Cutover Migration based on the number of users to minimize the downtime.

https://technet.microsoft.com/en-us/library/jj898490%28v=exchg.150%29.aspx?f=255&MSPPError=-2147217396

To support SSO ADFS must be in place or deployed before the migration.

The O365 Onboarding center will guide you through the whole process, Onboarding Center is included at no charge to all new customers purchasing 150 seats or more of any qualified license.

https://deploy.office.com/onboarding

Before suggesting the options, I would like to confirm, how many users you need to move from old server ?

For cut-over scenario, the above mentioned references looks a good start-up for you.

Step-By-Step: Migration of Exchange 2003 Server to Office 365: http://blogs.technet.com/b/canitpro/archive/2013/05/31/step-by-step-migration-of-exchange-2003-server-to-office-365.aspx

However, you may also checkout Exchange Server Deployment Assistant that is available from Microsoft team and would also be a nice approach. It covers all the required aspects and assist further by providing step-wise instructions: https://technet.microsoft.com/en-us/office/dn756393.aspx

As an alternative, you may also be interested using this automated solution http://www.exchangemailboxmigration.com/ that provides a hassle-free environment to accomplish the job in more easier way