I'll help if I can
I can't remember what comments I made back in '07, but if it was regarding an Aspera engine and oil, it would be something along the lines of "Check the oil as often as you can, as these engines like to through their con rod through the side of the engine casing if you don't"
As regards your Briggs engine, I expect that it will take around 1 pint of oil (most of those fitted to machines of that vintage do) You should find an oil draining square nut on the base of the engine (under the mower) a 3/8ths spanner should fit it. Always remove the spark plug lead when fiddling around with the engine, and tip the machine back onto it's handles so that the spark plug is pointing towards the sky. This makes sure that the oil that is in the crankcase doesn't go where you don't want it to! (IE= in the carburettor)
You can now undo the drain plug, and lower the machine back level over you bowl to collect the old oil, when finished, tip the machine back onto it's handles, and replace the drain plug.
Re-fill through the oil filler plug (normally plastic, and found on the crankcase-the other end from the spark plug) with 1 pint of oil (SAE 30) and bobs your uncle. The whole operation should take half an hour (taking into account grazed knuckles, swearing, scraping old grass and mud away from the filler and drain plugs, dropping your spanner into the bowl filled with old oil, and stopping for a cup of tea)
The engines themselves don't require any gear oil, some of the older Mountfields had a crazy drive box that went from the side of the engine to the front axle to drive the mower over the ground, don't worry too much if yopu have one of these, the gearboxes are "sealed for life" and shouldn't need any tinkering.
You should be able to find a manual on the engine. you will need the Model-type, and serial number from the engine, which you should find stamped into the metal of the engine cowling, often above the spark plug, or on the side by the exhaust.
an internet search should get you the information you need.
If I can help further, don't hesitate to call out.