OP to clarify you are just trying to have a completely local testnet set up to learn or do dev work on your local network?  I'd assume the dag in this case will be zero or very small and you should be able to mine on nearly anything.

Seems like the actionable error here is:  method eth_getWork does not exist.  How hard have you searched for this?

Another question, have you restarted or something after starting the geth instance the one time?  It may not be running at start so you need to check to see if geth is still running prior to starting to mine.