Right, compression is the first place to start. Since it has sat for 10 years I would spray some fogging oil in each cylinder before turning it over to test compression.
Next step, use a fully charged battery and an air gap tester to confirm spark on each cylinder. Also, install a new set of Champion QL78YC spark plugs.
Having sat that long I would assume the previous owner has used ethanol containing fuel which means the carburetors are likely full of gummy crud. I would rebuild the carburetors with new BRP kits, run through the fuel passages in the throttle bodies, and replace the o-rings on each fuel manifold. While the carbs apart check each float chamber for flatness. The carb mating surface on these plastic chambers was known to warp causing leaks.
Drain the lower unit and check the condition of the oil. If it's milky there could be damage due to water contaminated oil corroding the bearings.
Also due to age, I would order a water pump kit and install that to ensure you have good cooling. Remove the thermostat housings and make sure there is no junk causing the thermostats to stick.
Finally, if all the above checks out, pump all the old fuel out of the tank and fuel lines and refill with fresh non-ethanol fuel.
