But I'm determined to get it done.

Each and every deal comes down to these things to determine if the numbers work or not.If you are finding yourself wondering about either, I would suggest caution and patience.

Classes in my opinion are determined by class of renters, amenities afforded, and location. 

They charge 10% gross collected rent , and take 50% first months rent when they sign a lease. 

Then if we have agreed on a price, I pull out a contract and fill it out and have it signed on the spot.If it is a deal listed with a realtor, I might call them and give them a verbal offer.

That would probably be the easiest way to connect with some good PM companies in the South Amboy area and you can speak with them to determine who fits you best. 

Or at least the people that are signed on the lease.

The agreement I signed with the real-estate (property management company) says the Broker will maintain security deposits received from tenants in a trust account and will account to the tenants for the security deposits. 

What methods should I use to determine if the price of the house would be in the ballpark of what I would need it to be without seeing the house?

This seems like a red flag to me, and potential sign of a problematic tenant.