While researching on how to migrate all the files from share to SharePoint I thought about RBS as a possible solution. There are some user friendly tools out there like the one provided by Avepoint. It takes care of lot of back end stuff for you.
But do evaluate your need as RBS can also back fire. Check out this great article https://www.simple-talk.com/dotnet/.net-tools/sharepoint-2010-storing-documents-on-the-file-system-with-remote-blob-storage/ which explains RBS for SharePoint 2010 but the concepts are transferable to 2013.
It is better to import files from share to SharePoint so you can actually use all the features of SharePoint. Get rid of unused files , may be some of them can be lists, custom content can get rid of some more. Only import what is required.
Recently I came across http://en.share-gate.com/migrate-file-shares-to-sharepoint. If any one used it. Please post comments.