Everything here says Carb. Almost guarantee it. possibly accelerator pump, or power valve or maybe just dirty jets. First though, if possible, start from scratch on the current one. Warm engine, I assume the carb is a mercarb with one idle screw. turn that screw all the way in, snug, but never overtighten it. Be GENTLE and count the turns so you can reproduce what you have now. then take it all the way out and
look for anything other than a nice straight, sharp point. Screw it back in all the way and back it out one full turn and try to start it.this may take a bit, but it will never be right until it is adjusted correctly. The object is to get it to run, then get it warm, then get it to idle close to the correct speed. probably 550-750RPM. once that speed is close, you can adjust the idle screw in and out, to find the sweet spot. you my have to start at 1100 RPM and work your way there, but I have seen new carb that worked like crap until the idle was set. Many would-be techs will set the idle at 1000 to compensate for a junk carb that cant be made to idle. You probably need to rebuild your carb, but these things will need done anyway. Stop looking elsewhere until you have eliminated the carb. Mikes*
Welcome to Mike's Carburetor Parts - Your Number 1 Carburetor Parts Store *has kits and how to videos*
MerCarb Marine Carburetor Rebuild - Part 1 - YouTube *that make it easy and cheap. $40 for the kit. $20 for the soak solution at Walmart, some little brushes, and 4-5 hours for your first one. 2 hours after you get a little better. I'm no expert, but if you decide to rebuild it yourself, I would be glad to give you some pointers.