BE Upgrade and Migration to new server

Hi,

Customer is planning to upgrade their backup exec 12.5 to 2014 and to migrate to a new server. 

Would you recommend to upgrade the backup exec first to current server then migrate to new server or to migrate first then perform upgrade?

Current Server:

Memory 12 GB

OS Microsoft Server Standard 2008 SP2

Processor : Intel Xeon X5550 @ 2.67 GHz 16 CPUs

New Server will be Win 2008 R2

Memory of 16GB

Library: HP MSL G3 Series

Drive: Ultrium 4-SCSI / Firmware version (H58W and H68W)

Do we need to replicate/migrate existing BE 12.5 to new server with the Library attached to new server? 

Can we attach the library to new server after the migration?

Thanks!