Win2k3 will not run any version of Exchange except 5.5; I HIGHLY recommend you don't try to manually put it on there. If you must, upgrade the Exchange server to Windows 2000 (I did that myself and had no trouble). Save the new server to be a member server running Exchange 2003 (you'll be much happier if you do it this way).
First, you have to be running an AD domain:
I'd recommend you either add another new server as an NT4 BDC, or take a workstation for temporary use as a DC for the domain upgrade:
1. Install the server/workstation as a BDC.
2. After enough time passes for domain replication, promote the server/workstation to PDC.
3. Take the new PDC offline.
4. Upgrade the new PDC to Windows 2000/2003. This will upgrade the domain and make it easier to add Windows 2000 and 2003 computers.
5. If the domain upgrade goes properly (all user and computer accounts intact), reconnect the new PDC to the network and allow the domain to replicate. *Make sure WINS has a listing for the new DC in its entry for the domain, so the NT DCs can still find it.
6. Upgrade both the other domain controllers at your leisure (make sure each uses the new DC as their DNS server).
7. After both other DCs are upgraded, transfer all FSMO roles to them as well as the Global Catalog, and set them up as Active Directory DNS servers.
8. Set all clients to use the newly-upgraded servers for DNS.
9. Demote the temporary domain controller using DCPROMO and remove it from the domain.
10. If all your Domain Controllers are Windows 2000, switch the domain to "Native Mode".
Once that's done, add in the new Win2k3 server as a member server. Then, you can begin on the checklist included with the Exchange Deployment Tools:
Those tools will walk you through preparing your domain and Exchange Organization for the Active Directory Connector (which helps the Exchange directory and Active Directory stay in sync), and eventually help you migrate your Exchange organization to the new Exchange 2003 server.
I don't know about .PST files from experience, but you should be able to find plenty of info on it in Microsoft's documentation and Knowledgebase.