You can install Office 2010 without removing Office 2003. You have two options in that regard:
1. Replace Office 2003; or
2. Keep Office 2003.
With (2), you can use both versions, except for Outlook, for which only one version can be used. If you decide to install Outlook 2010, Outlook 2003 will be deleted and the PST files converted. You shouldn't need to change where you store your Outlook files, as Outlook 2010 will pick up your current settings (as should the other Office Apps).
See also:
http://support.microsoft.com/kb/2121447