The first step I would take is to test the Voltage output of the generator to make sure that it is putting out at least 42 Volts. Each battery in the pack needs to charged up to 13.8 Volts so a 36 Volt battery pack needs to be charged to 41.4 Volts in order to be fully charged and maintain the batteries at their proper level. If the generator is not putting out enough Voltage then the gear ratio between it and the engine needs to be increased, or a motor with a lower Voltage rating used.
There will also need to be a charge controller between the generator and battery pack to stop the charging when the Voltage reaches 41.4 Volts so the battery pack does not get overcharged. This charge controller could be as simple as a diode between the battery pack and generator and a Voltage meter on the handlebars that tells you when to turn off the engine, or as complex as a fully automated solar charge controller.
If using a diode between the battery pack and generator it just needs to be rated above the Voltage of the battery pack and above the Amperage that the generator produces. A standard power diode should work good for this application. Without knowing the Amperage that the generator produces the specifications of the diode can not be determined so I would start with an oversized diode like a 50 Amp 100 Volt or higher rated one just to make sure it can handle whatever is thrown at it.
Since you are using the battery pack to power a 300 Watt motor 7Ah or higher batteries will work great for that. I would not recommend using anything smaller than 7Ah with a 300 watt motor though.
The capacitors should be rated for DC power and should be rated for a higher Voltage than they will be used with. The uF rating of the capacitors could be any number. The larger the capacitor is the more energy it will store.
For a 36 Volt 300 Watt controller the gauge of wire between the controller and motor needs to be at least 14 gauge. The gauge of wire between the generator and battery pack depends on the maximum Amperage the the generator will produce when the battery pack is recharging. I would just go with a thick wire such as 10 gauge for this to be sure that it can handle what is being thrown at it.
If you are running a 24 Volt motor on 36 Volts then it may or may not be able to handle it depending upon the riding conditions and gear ratio between the motor and wheel. Heat is what destroys electric motors not Voltage, so the motor would need to not overheat when it is being used in order for it to work when running on 36 Volts.
A motor geared at cruising speed to consume 300 Watt running at 36 Volts will pull around 9 Amps of power.
It is not possible for a motor drawing 300 Watts of power to propel a scooter at 40 miles per hour because it does not have enough torque to overcome the air resistance (drag) at that speed. There is so much air resistance at 40 miles per hour that a motor with at least 3000 Watts would most likely be needed. A motor drawing 300 Watts could be geared for an 18 mile per hour top speed as long as it was used exclusively on flat ground and did not have to climb any hills or grades, if it had to climb hills or grades of any angle then a 12 to 14 mile per hour top speed would be best for that size motor.
My plans for a Gas Electric hybrid scooter.
I will be using a 1000 watt 36 volt DC drive motor as a generator that I got from a E-ZIP 1000 made by curry. I will be turning the generator with a 30 CC gas motor running on propane. It will be charging three 12 volt batteries wired in series for 36 volt. I then we'll be using a 36 volt controller that will be running a 300 watt high torque brush motor with chain drive to rear wheel. I will also be installing capacitors for starting storage for the Electric Motor. I have several questions that I need answered. Number one, I know I will need to install a diode between the generator and the batteries, what type of diode do I need, how many amps should the diode Be. Number two what should be the ahr for the batteries be. Will 7 ahr battery work, or should I go larger. What voltage should the capacitors be and what should be uf number Be. What gauge wire should I run between the generator and the batteries and the batteries to drive a motor. The voltage for the rear drive motor will be 24 volts will this be a problem? In theory I hope to have a Gas Electric hybrid scooter that will be quiet and have the range of the gas scooter. How many amps will I need for cruising speed? With the proper gearing I hope to have a top speed of 40 miles per hour and fast acceleration. My father who is electrical engineer but he's 91 years old has been helping me with this project. Like to know what you think, will it work ?? Need some advice or little help.