Un-tethered is better. With tethered you have to connect your iPhone to a computer whenever you want to restart the it. No reason to go with tethered, there is an un-tethered unlock for the latest 5.0.1 firmware.
No, you do not have to pay for a jailbreak, the software you will use to jailbreak your iPhone is free to download. Look up for "dev-team blog website" there you will be able to get the most recent redsnow tool available. Read instructions before start using redsnow.