I'm not going to go around in circles arguing the pro's and cons of tattoos. For the record, I don't think I would discriminate against anyone with tattoos or long hair/piercings, etc. Lots of my friends have tattoos. I just think it limits the kind of jobs you can get. You may love your current job but ten years from now you might want to change jobs and the extra ink could hurt your prospects.
It pains me to see young people in their teens or 20's making decisions that will potentially (detrimentally) limit their future career opptions down the road. Visible neck tattoos, sleeves or tattoos on the hands or lower arms will cause many people (including possible employers) to make unfavorable assumptions about you. It may not be fair but it's a reality. If I walked into a doctor's office and his arms were decorated like one of Jesse James' girlfriends (that bombshell chick and Kat VD), I might get a bit nervous.
Like everyone else, I made some bad decisions and mistakes I was a teenager and a young man in my 20's. Thankfully, none of these bad decisions required me to have a doctor painfully burn off large sections of my hide years later. Ouch...
Good luck with the sleeve, professor.