Running synthetics is always a good idea. If your engine is leaking the synthetic will probably leak more until it can condition those seals and stop the leak. A leaky engine needs to be fixed, not ignored.

Mobil is a good choice because it is readily available. Going with an oil that is hard to find might put you in a tough spot when it comes time to do an oil change.

Mobil 0w30 or 5w30 should work for most people in cold to average environments. People down south (Texas, Gulf Coast states, Florida) could run a 10w40 or 5w40 (0w40 is also out there) to offset the higher temperatures they see regularly.

Cheers,

Pete

 

I live in MI and I run Mobil 1 15w-50. Once you switch to full syn you might find that you use more oil than normal but that will stop once the engine gets used to the new oil.
The only reason not to use full syn is the price.
And Pete it right, pick a brand that you can find easily in your area. You can find Mobil 1, Pennzoil and Valvoline almost anywhere. Once you pick a brand stick with that brand.
Depending on how cold it gets where you are and how you drive depends on the weight of the oil that is right for you.