A push lawn mower is easier to store if space is an issue. They are ideal for smaller yards and come in many varieties. A riding lawnmower would be ideal if you have a large yard and space to store the mower isn't an issue.
Move your throttle lever back and forth and be looking at your engine. The other end of that cable (which will be moving as you move the throttle lever) is your carburator
That could be alot of things. Check under the deck and make sure the PTO is plugged in., it could be one of those wires are bad., check all your safety switches and make sure they are plugged in good...