It all depends on the size of your password. The encryption types are very different WPA2 can use a much larger key. I believe you should ask your parents about changing the security on their router before making any changes. You could possibly crash the router, then you may ruin the chances of a good birthday present.
Also WEP security is very insecure I strongly recommend not using it. If you get permission we can look into other options.
Edited: Grammer, spelling.
Edited by Sneakycyber, 26 January 2013 - 10:54 AM.