Is there a minimum value of assets that will eliminate the need for probate?

I am sorry for your loss.  Most every state has a probate proceeding for what is known as a small estate.  Every state is different, however, in what they think "small" should be termed.  In order to transfer any assets legally - by sale or otherwise - someone needs to be appointed as a personal representative of his estate.  In New York if you pass without a Will an Administration proceeding is what is begun.  Someone is appointed as Adminstrator (personal representative like an Executor) of the estate.  A petition much like a probate petition is prepared.  And instead of following the decedent's instructions as to who gets what the Intestacy Statute for the state is followed which lists who gets what. 

The first thing to do is to go to the Probate Court in the county in which he was domiciled (his permanent residence) at the time of his death and speak with the clerks there. Although they can not give you legal advice they can guide you through the process and quite possibly give you the paperwork you need to fill out.  You may want to consult a lawyer on a flat fee basis just to make sure that everything is legally correct.  Good luck.