Searching for my Grandpa's record

Lately, I am trying to find a hint about my maternal Grandfather. He lived here in United States for a long time. He died early so my mom had no opportunity to know everything about him. So far, what she knows were the lastname of the family who adopted my Grandpa and his name of course. I tried to do the international background check but I have to pay to use their service. I am saving some money and hoping that soon I get more information about my Grandpa.