Since it runs good once started, the most likely problem is a dirty carburetor. Specifically, the starting circuit.
That model has a fuel enrichment system that increases the fuel/air mixture when you go to start it. On an electric start, it is done automatically by the bystarter (white module on the top of the carburetor) or on a manual start, the "choke" knob does the same thing manually.
The carb bowl has a series of passages that feeds fuel to that area. It can be clogged and the motor can still run.
It is also possible that the auto enrichener could be stuck in the extended position, plugging that passage (although unlikely).
One thing to check that will tell you for sure that the carb needs work is to find the little plunger on the side of the carburetor. It has a little arm, that pushes a little silver plunger, surrounded by a little rubber bellows.
If it is stuck, then the accelerator pump is stuck and the carb needs cleaning.
It is not simple to clean. You need to understand the passages or you will miss one. Many on the forum can attest to that.
The Honda carburetor manual
https://www.amazon.com/Honda-Marine...TF8&qid=1465959213&sr=1-1&keywords=carburetor is the best investment to make if you are going to clean your own carburetor, it gives step by step explanations.
Mike