A clutch motor for a sewing machine simply engages and disengages the machine head from the motor. You can slip the clutch with the foot pedal to make the machine go slower, but the motor itself is always running at full speed.
The belt should be a "V" belt. I prefer a 3VX belt that is cogged, but it doesn't matter.
Do you know how to measure for belt size? Measure from the center of the motor's shaft to the center of the shaft the pulley is mounted on on your sewing machine. Say that's 13". Double it to make 26". Then measure the diameters of the pulley on the machine and the pulley on the motor. Say the machine has a 5" pulley and the motor has a 4" pulley. Multiply the two diameters by PI, divide each one by two and add the three dimensions together. In this case, 3.1417 times 5 divided by two equals 7.85 inches and times 4 divided by two equals 6.28". Add 26" plus 7.85" plus 6.28" and you get 40.13" You'd use a 40" belt in this example.
No one lives forever, the trick is creating something that will.