I agree that it would help to speak to others who have been in the same situation or even to a counsellor. You need to be prepared for anything I’m afraid.
He might not be the right person.
He might be the right person but deny it completely.
There might be a good reason why your mother wanted nothing to do with him. That may or many not still be relevant to you.
He will probably have another family or even families now and may want nothing to do with you.
He may have died, be in prison, be an addict or homeless or very unwell. He might be in debt and want money from you and harass you.
He may refuse to meet you, or agree to meet but not answer any of your questions .
Convsersly , he may want To meet you and your family and be part of your life and you might feel differently. He might want to bring you into his family and expect a level of contact or commitment that you don’t feel comfortable with.
You might meet him and find you dislike him or just feel you have nothing in common.
You should also research Genetic Sexual attraction, as this is much more common than people think .
Im sorry to sound negative, but It’s not all like on the TV shows where they only show you happy endings.
It can be much more complicated than people imagine, especially in cases like your where people feel there is something missing in their lives and start searching to find that “something”, whether it’s information, a relationship or a sense of belonging.
Remember this man has had nearly 40 years to contact you ( assuming that he’s alive ) and has chosen not to do so.
Do you have a partner and children ? How do they feel about your search ?