Well first off that's an Eaton compressor and up until recently they were recommended highly by almost everyone here because of their dependability and performance. Their reputation for reliability and performance is good however their attitude toward their customers may not be so good, they have threatened to sue Jon and this site because one of the members mentioned (just asked actually) that Eaton compressors are made in China which is true! Before you buy please read this thread and then make up your own mind if you still want to deal with these people.
Eaton Compressor threatens to sue me over "Made in China" compressor post
As far as your question about the pump we would need a lot more info on what you have but from your description of your compressor I can probably guess. I am thinking you have a 60 gallon tank (you said that much) with a two cylinder single stage pump and a 15 AMP motor. It may be rated as high as 6 HP, maybe even a bit higher, but that will be "Peak HP" and as such the HP rating is greatly exaggerated and completely useless. Look at the AMP rating on the motor data plate because that is what matters and just ignore any stated HP ratings, it is in reality only about 3 1/2 HP. If I am correct in my estimation of your equipment then obviously this pump is too big for what you have and will not work. Those Eaton pumps are generally over-sized anyway so they can be turned slowly which is a good thing but that would prevent you from using it by changing pulleys to slow it down even more, a method which is sometimes used to turn a large pump with a small motor.
A single stage pump is not quite as efficient as a two stage meaning the two stage will tend to run cooler, quieter, turn slower and generally can produce a little more CFM for a given amount of power. The two stage pump will also generally last longer and be slightly cheaper to run due to it's better efficiency and a two stage can also be used to produce a higher top pressure, usually ranging from around 145 PSI to 175 PSI while the single stage will top out at about 125 PSI. The 125 PSI is high enough for most anything you will need it for however but the higher pressure of the two stage will serve to store more air volume for a given tank size. Since the two stage can compress air more efficiently at higher pressures this will allow for more air volume for the amount of energy used.