Be sure not to get in the tanning bed too long the first time. I think it's like 3-5 minutes your first few times. Also, you really SHOULD wear your eye protection!!! If you want minimal tan lines, wear a thong...or you can place a small (or large! ) towel on your penis to avoid a white ass.
A lot depends on how white you are and what tanning bed and setting you use.
I only tanned a handful of times, and went naked each time. My pee pee never burned, but it got really dark brown! But then again, I'm half Indian (and white), so I'm naturally a little darker. It might be different for you, depending on your complexion.