How to backup an iPhone, and restore it, with no side effects?
You can use a computer for backup. It only ties for that computer in regards of music and video content. If you want to sync it to another iTunes library at a later point, the music that was synced from that computer will be deleted. This is not the case for tracks bought in iTunes if that device is activated for that account, or if you're using iTunes match.

If you use the computer, you can choose to encrypt the backup, that way the passwords (for networks and whatnot) will be backed up and restored as well.

As a side note, it doesn't seem usual to me that you need to restore the phone for the unlock to take place. It usually is enough to connect it to a computer with iTunes open.