I'm really unsure of what category to put this in.

The business next door to us wants to erect cranes to complete their building project. They have contacted me and three other neighbors, in person. Their cranes will pass over our houses during 20 months of construction. They want to rent the air space and are prepared to compensate us.

What type of compensation should I expect or ask for? What type of safety issues should I be worried about? Should the four neighbors involved present a united front? Do we need a lawyer?

Thanks.

I vote for getting together and hiring a lawyer.
I don't know the lay of the land but I can't think of a good reason for them to swing loads over adjacent properties. Do they plan to reach across your property to another lot on the other side of your property, to pick up materials? What liability will they have if damage is done to your property? My first reaction would be--No, thank you!

They said that no heavy loads would be moved while the crane was in my airspace, just the boom?

Of course, the boom itself is a very heavy load. Maybe it is the counter weight of a stiff leg crane (like the ones used on high rise construction). There are accidents all the time with all types of cranes.
How does your homeowner's insurance agent feel about it?
Chances are the contractor has other ways to complete the work without bothering you folks.
They usually do what is easiest and cheapest for them.
I would talk to the neighbors involved and see if they will split the cost of the lawyer. And see if you have some options. You also may want to contact OSHA (or other safety agency) to see if this is in compliance, ageement or not.