How to migrate data of to another sql server
For very large Databases you can always use the compression method in SQL server 2012. That will help a lot in reducing down the backup size of the database:


For how to use and more on this refer to below link:

http://www.sqlservergeeks.com/sql-server-database-backup-compression-faster-disaster-recovery/


To avail the space, make sure you're backup retention period is appropriate so as to make proper amount of disk space available.
If possible do some TPM like cleaning activity on the disk to get some space.
Also, for data level compression you can just script out the schema and then move data using BCP OUT and BCP IN. You can even zip those files and move them across the destination server.
Last but not least: One more thing to add :


Make sure that Instant File Initialization is enabled on the server. That will dramatically reduce the restore time. Refer to below link for more info on this..

http://sqlblog.com/blogs/tibor_karaszi/archive/2009/03/09/do-you-have-instant-file-initialization.aspx