Hello
Thank you for reaching out.
In my experience its all depend on your IT environment and demand of data.
You need to decide which type data they are (SQL, Files, Emails) according to your company and customers compliance policy.
to save costs you can buy some cheap NAS or SAN appliance and move those data for archival with some basic Redundancy.
if the data are not huge in size then you can Move it to some Local disk storage Fileserver and delete it from Original location.
You can create Archive policy specifying what kind of data it would be arching and at what schedule.
Hope this will give some idea regarding Archiving.
Thanks,