You don't have to pay any part of your finds to either GPAA or the claim owner, if it's listed in the guide.
You are, however required to follow all state and federal laws and regulations. This includes anything required for equipment such as a dredge permit or highbanker permit. Some states regulate sluices and pans even, so do your research on the area you're going to.
Here in Oregon you are supposed to have the 700PM permit for dredging....$500 for the first year, and around 85-90% of waters are closed with varying seasons on what is open. Need the 600 permit for highbanker, not issuing at this time, but existing ones are still valid.