Any or all of these may be the problem...

Battery connections at BOTH ends.

Battery

Solenoid

Starter

If you don't know enough about small engines to diagnose then get it to the dealer.

Sounds like the carb is leaking fuel into the engine while it is stored between uses.
The reluctance to crank initially may be due to the cylinder being hydrolocked with gasoline.
After enough attempts by you with using the starter, the fuel slug in the cylinder is expelled, but the engine is flooded so it requires extra cranking to clear out enough fuel so combustion can begin.
Then comes the big puff of white smoke as the fuel and residual junk in the muffler burn off.
You need to add an inline fuel shut off valve to the fuel hose between the fuel filter and the tank. Turn the valve off every time you stop the engine.
The needle valve in the carb is leaking fuel is why the problem occurs.
You can fix the carb if you like but you must add an inline fuel shutoff valve and close it except when the engine is running.
You also need to change your engine oil and oil filter (if it has one) before you operate this engine again.
If your carb has been drowning the engine when parked, there is gasoline diluting the oil and that will spell engine failure.

Don't buy one unless you are mowing a dry, level area. We use the tractor to pull a small cart around our farm and it is horrible to steer on anything wet and is constantly getting stuck in mud and snow unless I keep the chains on it. I wish it came with ag tires. That said, it has been dependable as I've maintained it according to the service schedule, replacing only the throttle cable (easy) and the battery in five years and it works hard.