Have you downloaded or bought a service manual for it yet? Mandatory first step.
You didn't mention taking the carburetor apart for cleaning. No way you can avoid it.
To begin with, you don't have a "tuning problem." The carburetor leaking fuel out the overflow is not a tuning problem. You have to fix that before you do anything. In all likelihood, the float is either stuck, or there is dirt in the float needle. You have to take the carb apart, clean all passages with carb cleaner and compressed air. Adjust the float level. Here is where the manual comes in. Set the float level according to the manual. Then, after it's all back together, you may have to adjust the idle air screw mixture screw to optimize the idle. That should do it. The "air/fuel" ratio is fixed by the jets that are in the carb, and no need to change those jets unless you change the air filter arrangement to allow more air. If you stick with stock air filter, the float level and idle air screw are your only adjustments.