Rent agreement

copy is fine.

if possible, make sure the deposit is made via check..

Original deed is always kept with landlord.Get a photostat copy[certified by Notary Public] of rent deed.

Normal procedure is you should type the rental agreement on two sets of NJ stamp papers (i.e. two original sets) but in your case, you have made only one original set, in this case, I advise you as shown below.

Photo copy is ok, but take original signatures of the Owner and you make your signature beside the signature of owner on each and every page.  This is sufficient.  Notary is not compulsory.

You can ask the landlord to sign on each and every page and you also put your signature beneath it in the photostat copy of the rental agreement held by you, so that it becomes valid and all your problems in this regard  can be set aside.