Sql-server – have to change Media Sets to create a Full Backup to a new file and what does that mean

You will need to set up a separate backup device for the FULL and the DIFF. When you create the Backup Device it is a single file. You can't save a FULL and a DIFF in the same Backup Device.

More information about backup devices can be found here: http://msdn.microsoft.com/en-us/library/ms179313.aspx

If you are trying to restore the database over an existing database and want to replace the data you will need to use the WITH REPLACE option in the restore. More information can be found here: http://msdn.microsoft.com/en-us/library/ms186858.aspx

REPLACE should be used rarely and only after careful consideration. Restore normally prevents accidentally overwriting a database with a different database. If the database specified in a RESTORE statement already exists on the current server and the specified database family GUID differs from the database family GUID recorded in the backup set, the database is not restored. This is an important safeguard.

The REPLACE option overrides several important safety checks that restore normally performs. The overridden checks are as follows:

Restoring over an existing database with a backup taken of another database.

With the REPLACE option, restore allows you to overwrite an existing database with whatever database is in the backup set, even if the specified database name differs from the database name recorded in the backup set. This can result in accidentally overwriting a database by a different database.

Restoring over a database using the full or bulk-logged recovery model where a tail-log backup has not been taken and the STOPAT option is not used.

With the REPLACE option, you can lose committed work, because the log written most recently has not been backed up.

Overwriting existing files.

For example, a mistake could allow overwriting files of the wrong type, such as .xls files, or that are being used by another database that is not online. Arbitrary data loss is possible if existing files are overwritten, although the restored database is complete.

I would say that there isn't necessarily a Best Practice, this is more of a matter of personal preference or your businesses operating procedures. I've had separate folders per database, then sub folders for FULL, DIFF, LOG at some jobs, others everything goes to a single folder and the backup name is some combination of database name, backup type, and datetimestamp to make each file uniquely named. I'd recommend looking at Ola Hallengren's maintenance solution:

https://ola.hallengren.com/

This is what I recommend to all my clients for database maintenance and backups and it handles everything dealing with the file naming and folder structure automatically for you. Just run his script and set the jobs to run at the frequency and schedule that meets your requirements and you are all done.