I think a 40:1 gearbox might be a little slow for a band saw. 10:1 would be my first choice, then do the final reduction between the gearbox and the lower wheel shaft with pulleys and belt.
But first you need to do a little math. You want a speed range from about 60 - 400 FPM (Feet Per Minute) for metal cutting.
First let's look at the wheel diameter, you need to know the circumference of the wheel in feet, so, (Pi x dia [in inches]) / 12 gives you the circumference in feet. So let's assume a 14 inch wheel. (3.14 x 14 = 43.98 inches) / 12 = 3.66 feet. so if the wheel is turning at 1 RPM, the blade speed in FPM would be 3.66. at 10 RPM would be 36.6 FPM and at 100 RPM would be 366 FPM
Now let's look at the motor RPM, the motors that you would want to use are 1725 - 1750 RPM or so, but to make it easy let's use 1800 RPM because that is the synchronous speed of the motor. So with a 10:1 gearbox, the output shaft would turn 180 RPM So 180 x 3.66 = 658.8 FPM with a 1:1 ratio on final belt drive or 329.4 with a 2:1 ratio on the final belt drive.
Using stepped pulleys, you can get various speeds by changing belt positions. This is what I have.
A treadmill motor would be a good choice and there are controllers available for them on Ebay.
If I really wanted to do a Cadillac system. I would use a 3 HP 3 phase motor, a sensorless vector VFD, and a 10:1 C-face gearbox. This would give you a usable speed range of about 5 to 1300 FPM.
A C-face is a standard motor mount arrangement where the motor bolts directly to the gearbox.