I have three tattoos and I'm a nurse. Two of them you can't see and one is on my inner wrist. I would recommend getting your tattoo somewhere that you can hide it if need be. After you are established in your job, it probably won't matter.
Road is my favourite and it's best to ride not drive so you can enjoy the changing views along the way. Train is great because of the large windows. And yeah - you never drive that.
I always prefer the train if possible.