I'd say go for the position that's more towards the inner part of your arm/elbow (the first option you talked about). I always like the way people get tattoos done on like the inner side of their arms like that. Easy to conceal, and just as easy to show.
Don't listen to the other guys - whether or not they feel you should be getting a tattoo is irrelevant, especially if you're already set on doing this.
Nothing wrong with your hair..you a pretty, sexy, female...why do you want to disfigure yourself? I saw a pretty gal at the pool today...she would have been too skinny for a lot of guys but I adored her...and she had on a one-piece but with a neck strap...so back was bare...except for an ugly tattoo on her right shoulder blade...ugh...if a female MUST get one of the ugly damned things then should put it where I don't have to look at it...o.O
Your last bit, I would say put it up a bit on your arm so it can't move but, one thing I will say is keep it visible for you! Don't put it slyly on the back 'cause let's say it gets infected, or you need more color on it, whatever, you don't know unless YOU can see it. Plus, if you're getting a tattoo you're gonna wanna look at it for a bit.