I can attest to the fact that laser tattoo removal is FAR more painful than laser hair removal. It is also extremely expensive.
So just to be safe, if you do get a tattoo don't get one with red ink in it and limit the yellow if possible. Red just can't get removed with today's technology and yellow is only partially removed. I'm likely to have what looks like a small bruise on my arm due to the yellow in the one I'm having burned off.
As for the placement, just keep it off of anything you really expect to grow when HRT does its thing. Arms, ankles, back, and abdomen should be pretty safe.