The throttle linkage is fairly basic, but can sure seem strange at first. Let me know how much you know about them, but I will give you some basics now.
If I need to elaborate, please feel free to ask..If I give too much detail, please forgive, just trying to help.
The key to the whole thing is the throttle butterfly. It is inside the barrel of the carb, you can't see it when the carb is installed, but it is actuated by the throttle arm which you CAN see. They are both on a common shaft.
The throttle arm also has an idle limit screw to control how far the throttle can close (Just enough for a steady, even idle when warmed up).
The throttle arm should be linked directly to the governor arm which sticks out of the crank case. Usually fairly long, several holes in the end to allow a variety of strengths of spring.
There is also a "Throttle Spring" that connects to the "Throttle Plate" which is actually another moving arm. The Throttle plate also has a stop to limit how high the throttle can go (the 4 positions for the stop screw on yours), and sometimes a kill blade that is connected to the ignition coil, and is grounded by the throttle plate when the throttle is set to the 'Off" position.
The throttle plate is also the piece that your throttle cable connects to.
The Governor arm often doesn't feel like it does anything until the engine is running. Then, it pulls toward the low throttle position, closing the butterfly down to the idle position as set by the idle screw (Not to be confused with "Idle Mixture" which sets the lean/rich mixture at idle).
When you throttle up, you are pulling the throttle plate, which stretches the spring between the throttle plate and the governor arm, thus pulling the governor arm away from the idle position, and increasing the engine speed.
Once the speed has increased, then the spring and the governor find balance at the new RPM. More spring pull, more RPM. etc.
Sometimes, the spring pulls on the throttle arm instead of the governor arm. While possible, this is NOT recommended because a failure of the linkage can cause a "Runaway" condition which usually results in a spectacular and highly dangerous destruction of the engine!
Ok that should be good for starters. Once everything is in order, you should limit the high end to 3600 RPM, the design speed for most domestic 4 cycles.
If the linkages and spring are all just right, the throttle should be smooth, even, and linear through the entire range.
Coat hanger for big engines, and bike spokes or stiff music wire for the smaller engines, a couple pair of needle nose pliers and a cutter, and you can make the linkages you need. Just be sure the governor arm can pull the throttle arm all the way to idle, or the idle may rise and fall by itself.