Some of the things that you need to consider before upgrading your Windows 2003 Domain to Windows 2008/2008 R2 Domain
Below are some support articles that can help you in your planning for the upgrade:
https://support.microsoft.com/kb/946405
https://support.microsoft.com/kb/942564
https://support.microsoft.com/kb/944043
https://support.microsoft.com/kb/977321 -
And you need to make sure that all AD Aware Applications will work fine with Windows 2008/2008 R2 before deploying Windows 2008/208 R2 Domain Controllers.
And please use the below post as your guide for upgrading to Windows 2008/2008 R2 https://technet.microsoft.com/en-us/library/upgrade-domain-controllers-to-windows-server-2008-r2(WS.10).aspx