Welcome (almost) to NJ !
I strongly feel you need to have an agent working with you who is an expert in a particular area. Because of that, I urge you to find agents in each of the areas you mentioned, as they are NOT interchangeable, and no one agent can really cover all of them...and cover them well (no matter what someone may tell you)!
For example, I COULD show you homes in Westfield and Edison, as they are part of my MLS system, but I really don't know those towns well enough to really get you educated on them. You need an expert - an agent who has their finger on the pulse of the town. My "finger" is on the pulse of essex County and lower Morris County which have a few towns you might want to consider. The 3 towns you mentioned all have vastly different flavors to them.........so you need to take a look and explore your options.
Especially considering you are moving here from CT, you need someone who can point out all the different nuances of each area....schools, shops, what the different sections are, etc.
Now....how to find an expert for each area?
I am sure some agents will come along here who can help you. Check out their websites and ask them how much business they did in a particular town. Make sure they are an area specialist.
When transferees are assigned to us - moving here and working through a relocation company, they are always handed off to different agents for different areas.
No one agent can be everything to everyone!!
Another thing you can do is look at some larger company websites... such as mine (Prudential NJ Properties - of course!!), Coldwell banker, Weichert, etc..........check out the individual offices they have in the towns you mentioned. Look through the list of agents in those offices, and their levels of experience. You could even call the Managers in those offices, and ask them for suggestions and names of agents.
I can offer some agent suggestions for Westfield and Edison.... agents I know personally, who are really experts those towns. I can't help you with Secaucus, as I don't personally know anyone who specializes there, but I am sure some will come along here.
Interview everyone (start with email and phone).............see how responsive they are to you, and see if you "click" with them.
I am not sure of your price range......so, there might be some towns you haven't mentioned ( Millburn/Short Hills, or Chatham& Madison for example)) that you might want to add to your list. I can help you with those towns, or certainly help point you in the right direction.
This is a lot to digest.........find a few agents who will help you, and in time, you will know what town is right for you and your family.
All the best with your move....hope this has helped!
Good luck............and I would be more than hapy to help you if I can!
Prudential NJ Properties