You are not really at the best starting point.
The most compact way of getting a 30:1 reduction would be a worm and wheel. But this would mean your motor sticking out at right angles to the machine. (Unless you fancy having two worm boxes, say 6:1 feeding a 5:1 to bring the drive lines back parallel again )
For 30:1 with belts you would need at least a two stage drive, again a 6:1 and then a 5:1. With a minimum pulley diameter of 1.5 inches,the driven pulleys are still going to be pretty large,, 7.5" and 9 " diameter.
Assuming that you are using a standard 12" hacksaw blade, a Z section belt would probably cope with such small pulleys.
Polyvee belts might be better, for small diameter driving pulleys..
With small driving pulleys, to increase the wrap around the pulley, you will need fairly long pulley centres.
A four pole motor with a nominal 1475 rpm would halve the ratios needed, allowing driving pulleys of 2" minimum, and smaller driven pulleys..
If the motor can be mounted under the machine, it could drive to the countershaft at the rear, to make things compact.
Howard