I myself work in a tanning salon, there are a lot of myths out there. If you use tanning in moderation it will not have any effects, short or long term, on your skin. Just make sure before going in you put on a good lotion / moisturizer, ask the person behind the counter to buy some lotion with "bronzers" in it, and dont cheap out and get the most inexpensive lotion there...because it probably will make your skin orange if your paying 3$ for a packet of lotion.
A few hours after tanning make sure you put on some type of moisturizer, and after getting out of the shower as well.(chlorine will dry up your skin) This is the important part, this is the part that will save your skin in 10-20 years...and this also helps you keep the tan longer.
Also, dont go in the cheapest bed they have, they'll throw you in there for 20 minutes and you'll fry your skin. Shell out the extra money and use one of the better beds, ask them to tell you about there products. Research the tanning salons in your area, ask your friends, or even ask strangers about it...because a lot of places are **** and don't change the lamps in the beds and you are basically wasting your money away.
When first starting out go every other day until you get a base tan, when your satisfied with the tan you have, go every 3-4 days, try not to go more then twice a week. (again if you pay for the cheap ****ty beds, your gonna get a cheap ****ty tan that fade's faster....the more you pay, the better the tan, and the less you have to go)
Going tanning can actually be healthy for your skin if used in moderation, your skin takes in vitamins, and your brain will release endorphin's which will actually make you feel better about yourself.
(oh and about being naked......just take your sock and put it over your more private part's, the skin on your penis is very sensitive and it will get dry and irritated with over exposure.)