Ubuntu 12.04 here. Unity is a beautiful desktop for development - just keeps out of the way and text search is excellent. I used Mint for years, but find it incoherent in comparison, and don’t get me started on their approach to LTS - a number of bugs in the previous Mint LTS software that were never fixed.
If you go Ubuntu or derivative, my advice is stick to LTS releases for development.
Never had much issue with AMD graphics - never owned NVidia so maybe I’m missing nirvana!
I use NetBeans with OpenJDK. Not had any problems with OpenJDK for years, and if you go for 7 you shouldn’t have much issue - OpenJDK is the reference implementation after all. Don’t use applets much or webstart so not sure what the support is like - the sooner applets die out the better anyway!