Start out with the pipe and muffler that came with the engine. From your description of the air cleaner my guess is that your carburetor is probably the old NT style, which I and many others feel is the best option, especially for a beginner.
It is easily tuned and typically performs well under most conditions. There is a lot of good information here about that carburetor but to start with you'll want to have the little clip on the needle on the second notch from the top. That's a good starting point. The clip determines how far the needle is lifted when you twist the throttle grip. The lower the clip, the higher the needle is raised and the richer the fuel/air mix delivered to the engine. Conversely, the higher the clip, the leaner the mix. The needle only controls fuel flow up to about 3/4 throttle and after that the jet orifice size determines fuel flow.
Mix up a new batch of fuel in a serperate container then drain your tank and refill with the new fuel. You can get rid of the old stuff by dumping it in your car's fuel tank. It won't mind a bit.
Tom