Best practice - Log shipping / replication for archive / reporting database
I would recommend to use log shipping but only if you do not want to prevent delete operations. Log shipping keeps the target database the same as the source database.
Log shipping is a relatively simple mechanism, it just backups and copies over the transaction log and applies it to the target database. It is a bit simpler to setup and to maintain than Replication.

Replication also keeps the source database completely in sync with the target database. With transactional or snapshot replication there is no possibility to exclude delete operations.
The only exception is that in merge replication exclusion of DELETE statements is still possible. However, this possibility will be removed in future versions of SQL Server (see the first note in https://msdn.microsoft.com/en-us/library/ms146947.aspx). So that is nr. 1 of your worries I think. Some more considerations can be found here: https://technet.microsoft.com/en-us/library/ms151206(v=sql.105).aspx.

Performancewise there also can be a big impact. This depends a lot on the database and the operations on it. So test it in a test environment to see if the performance loss is acceptable.
Personally, I'm not a huge fan of merge replication as I have experienced many problems with it.

Summarizing, if you want to prevent delete operations I would recommend to write your own synchronization mechanism. If you don't want to do that, and can live with the issues mentioned above, merge replication will also be usable.