Having the server version, you have two options in which you can view a report.
1. Managed(By publishing the report to the Crystal Report Server 2013 repository)
2. Unmanaged(Report not published to the repository)
Whatever approach you choose, if you are moving from CR4E to Crystal Report Server, you would need to use the jars provided by the Crystal Report server.
The list of jars which would be required can be found from the developers guide of BusinessIntelligence Platform Java SDK guide. You might want to look at RAS SDKs along with viewers SDK which is used to export the report to pdf or view a report in the viewer.
Samples are available at
http://www.sdn.sap.com/irj/boc/index?rid=/webcontent/uuid/f0aea666-5384-2b10-ffb0-a6facef1d5e5
The samples are for XI 3.1/Crystal Report Server 2008 version, however can be used for 2013 version as well as there is not much significant difference.
The only thing to keep in mind is to use the crystalreportviewers folder and jars from the current version.
It would be best to explore the developers guide to understand it better.
You find the guides at http://help.sap.com
Navigate to Analytics--> Business Intelligence Platform(Enterprise)--> Select the version and refer to the Development section.
Regarding the deployment of your WAR, you can choose any approach, either have it installed on the tomcat which comes bundled with the server or have your own stanalone app server and deploy it in that.
Thanks,
Prithvi