Since your just looking at an Oil Change, I would recommend your selling dealer. 1. The have the most to gain by making you a service customer. 2. I would rely on them having the smarts not to mess with the car. 3. The oil change is a no-brainer. 4. You know they are using the correct oil and filter. I would stick with Fords latest 5w-50 (rec.). It is made by Mobil as is all “Factory” oils. Toyota is now using a 0w-16 (yes 16, why 15 wouldn’t work I don’t know).I don't see very many GT350s running around, and I wonder how many of the local Ford dealers have much experience with service.
Recommendations? Dis-recommendations? PM if you're not comfortable blasting someone in public.
Beyond that, no hints sorry.