I want to have goats (horses, chickens, etc), what are the rules?

In Plaistow we do not regulate the animals, we regulate the structures for the animals.

Yes, you need a permit to put up a barn, coop, shed that will house an animal (other than your domestic cat or dog).  

Structures for smaller animals, like chicken coops and rabbit hutches, need to meet the regular structure set backs for your district (35' from the front property line, 15'/25' (MDR/LDR) side and/or rear property lines and 75' from wetlands) - Hang on to these dimensions, they are the same for any structure you might want to put on your property.

Structures for larger animals, like goats, sheep, cows, horses, etc have the same setback in every district. The shed/barn must be 100' feet from all property lines and 75' from any wetlands.  The corral/fencing must be 50' from all property lines.

If you have an existing barn on your property, unfortunately you cannot use it to house animals unless it meets the above setback requirements or you are able to obtain a variance from the Zoning Board of Adjustment.

Of course, you should be a good neighbor and design your waste disposal methods with them in mind.  And always treat your animals in a kind and humane way.