I have done this before, so I did my research before i tried it, good thing u r asking too! go with facebook, because it is a proven fact that myspace has found a way to give u a virus no matter what spyware program thing you have. Don't give ur account a profile picture, obviously they will be able to recognize you from that, but you can upload a cool picture for it just not one of yourself,go into settings and make everything private, so that only friends can view ur page,ur info, stuff like that, then, put down something for ur name that is not ur real name, something like "sexigirl" or "hottstuff", better if it is something that is not like you so ur parents cant find u, u probably don't want to have ur settings so that u cant be searched for because then u have to find ur friends, then last, tell all of your friends the name that you picked for yourself so that they can search for you, then, once a month ask your parents for a facebook page, and if they finally say yes, set up a new one with your REAL name and your picture, and search for your friends, and voila! Hope this helps! Also set up a new email for it, use the new email just for facebook, cause then ur parents cant crack ur email and find facebook stuff in it!
experience; and it worked!