My opinion (experts correct me if I am off on this) - the "secondary" server when doing log shipping is usually in place for disaster recovery. If the primary server tanks itself for some reason, you want this secondary to pick up the slack.
Due to that, my recommendation would be to make sure it has the SAME resources available than the primary.
Now, the "bare minimum" for the secondary would likely be the bare minimum for SQL Server 2008 R2, but as soon as this secondary needs to become the primary, you are going to regret using the bare minimum.
As for the licensing model, if you have software assurance, then the secondary is free (I believe? Not sure if that applies to 2008 R2 or not). But that is a VERY loaded question. Does your primary use features of Enterprise edition? then the secondary should be on that version too. if your databases are small (under 10 GB) you may be able to get by with express (NOTE - not sure it supports log shipping).
For licensing questions, I strongly encourage you to reach out to your SQL Server licensing vendor as they may be able to get some deal for you and WILL be able to provide you better advice than the forum will.