It is highly recommended to do bit cleaning before you do an upgrade of SharePoint 2010 environment to SharePoint 2013.We need to make sure that environment is running and fully functioning, and should clean up all those contents which doesn’t required upgrade.

You should consider the following items to clean up before upgrade.

• Delete Site collections/Sub sites which are no longer in use
• You should consider moving site collection into separate content databases for better performance and scalability
• You need to remove unused custom features, web parts, templates, event receivers, workflows etc
• Make sure if you have large list (Lists with a lot of data in it), user should not be able to query data which exceed the threshold limit set on Web applications
• Document versions can slow down an upgrade process. If you do not have to keep multiple versions, use the object model to find old versions and remove them or ask users to delete unnecessary documents version manually
• The default authentication type in SharePoint 2013 is “Claim based”. You can still create web application with” Classic authentication” in SharePoint 2013 through PowerShell, but it is recommend using Claim based Authentication in SharePoint 2013 web apps for variety of reasons.  Also, windows Classic mode authentication is deprecated in SharePoint 2013.
• You cannot upgrade “FAST Search Centre” sites to the SharePoint 2013 environment. The current “FAST Search Centre” sites can continue to work in SharePoint 2010 mode after upgrade. If you want the have new SharePoint 2013 functionality, you have to create ” Enterprise Search Centre” sites in SharePoint 2013 mode.