Hello,
R12 is no longer bleeding edge, it's all quite stable (as stable as Oracle gets anyway) now. I would suggest you go 12.1.1, as, exactly as you noted, if you go 12.0.6, you will just have to go through another upgrade in 6 months or so. Also, Oracle will always suggest the latest family packs as solutions when you encounter problems.
Not meaning to be cynical, but maybe Oracle Consulting are looking to an opportunity to maximise their revenue stream with the further potential upgrade from 12.0.6 to 12.1.x in the future.
However, having said that, you should check that there is an upgrade path from your current version to 12.1.1. There is always the possibility that you are restricted to upgrading to 12.0.6.
Regards,
Peter.