I run ME880s on mine, 170 rear, stock 110 in front. Going with the 120 front tire will screw up your speedometer, and a fatter front tire will just serve to make it "flick" slower. Fatter rears have a similar effect, but the Max needs all the traction it can get.
Some have reported that a Lasertec front can help with "the wobbles" this bike is known for.
I would go with a 170-80-15 rear and the 110-90-18 front, both ME880's. Expect to use two back tires to one front, maybe three if you like to do burnouts a lot. I've got nearly 10k on the front and I'd guess it's maybe at 50%. This rear has around 3k on it and is just starting to show some wear.
I ride hard, lots of high speeds and "brisk" acceleration, but I do try to keep wheelspin to a minimum and that's what trashes tires. One good smoky burnout and BAM! there goes 1000 miles of life.