Using a stabilizer will extend the storage time of fuel. That said, the fuel tank and carburetor of your new Honda mower are not a good place to store fuel. :thumbdown:
If you don't expect to use the mower for at least 30 days, drain the fuel from the tank (or let it run dry) and also the carburetor. Instructions are in your owner's manual.
You can use stabilizer to treat the fuel you may have in a fuel can, but if you expect it won't get used within 60 days, you should dump it into the tank of your vehicle.
Generally, the only trick to starting up a new mower (or one that's been drained of fuel) is to give the fuel a few seconds to drain from the tank down into the carburetor. Fill the tank with fresh fuel, turn the fuel valve to ON, then wait about 30 seconds. Be sure the choke is set to ON (closed) if your mower has one. Grab the recoil starter handle and pull it out gently until you feel resistance. This removes the slack from the cord and makes it less jerk/effort to start the engine. When the engine starts, slowly allow the cord to be pulled back, don't let it snap back to avoid damage.
Properly configured (choke, fuel, etc.) most Honda engines will start in 1-2 pulls. If not, recheck the choke, fuel valve, fuel supply, etc....they are almost always the reason the engine won't start right up.