Rob, I suggest you divide the project into two phases: getting the engine working, then getting the mower working. Can you declutch the engine, and rotate its crankshaft without driving the mower? If so you can go through a simple engine checkout, which needn't be as elaborate as your list unless you will enjoy doing that stuff. If the engine is full of decent-looking oil, its crankshaft rotates freely, it is disconnected from the mower, and it has a clean petrol tank, you can put fuel in and try to start it - after you are sure you know how to stop it. B&S engines normally have a kill switch that shorts out the ignition. Never start an engine until you know how to stop it - preferably, several ways to stop it.
Once the engine is running properly move on to checking out the mower - which you do initially without running the engine. With the clutch disengaged, you try to rotate the non-engine side of the clutch by hand, seeing what happens and how easily it turns. If everything turns steadily without resistance or strange noises, it is time to run the engine and engage the clutch. Having accomplished that, it is time to start cleaning it all up, lubricating it, and checking the adjustments.
