What is the best way to thank your GM?
As the constant GM, I don't know. I've barely ever had to do this...
How would I like to be appreciated?
In some games, I've provided the game, while someone else has provided the house (or relevant gaming space), and everyone else has provided the food and drinks. It was nice having everyone share the load for the evening then.
In other games, I have been paid to GM, it wasn't asked for, or necessary, but certainly wasn't turned down when it was offered.
Lately, just engagement in the game, actively joining the events and contributing to the storytelling has been the best I've been able to hope for from a group. I'd start actively recruiting a new group of players, but need to focus on Uni for the next six months before I get a new game up and running.