It could be other things too, but I would start with checking out the carburetor. If it idles okay but then stumbles while you're pushing the pedal to accelerate and then recovers once you get up to a steady speed. Then its most likely the accelerator pump. The engine needs this extra squirt fuel to make the transition between idle circuit and the main circuit. If it's not working it will cough, puke and fall on its face like it's running out of gas while the gas pedal is moving until the main circuit takes over and then it runs fine. With it shut off, pull the air cleaner and look into the carb and you should see a squirt of fuel when you move the linkage. It's really common for a carb to sit and the accelerator pump dries out and shrinks and it won't squirt. If it's not squirting than I would go ahead and rebuild the carb. Just be gentle with all those little screws, it doesn't take much to strip them out. Blowout each of the fuel passages with a can carb spray with the straw nozzle. Put the straw up against each port and make sure it blows out the other end of it. Then you'll need to set the choke level, Idle air fuel adjustment and then finally the idle speed.