Formula to Match DC Motor Size & Gear Ratio for Generator to 110V AC Output

I have a generator with a performance profile to include horse power and torque for a given set of RPMs.  This generator will drive a DC motor.  I'm looking to determine the specific type and size of DC motor that will most efficiently produce electricity given the performance profile of my generator.  This generator will be intended to power 110V AC household power.  I'm looking for help on the following:

what is that formula?

is direct drive or a gear ratio better?

if it's better I use a gear ratio what is the formula to determine the most efficient ratio?

thanks in advance