1700's drum table

My grandfather's name was Karl Greene. My dad was born in Buffalo but had his name changed when his mother remarried. We had an heirloom when I was growing up that Thomas Jefferson gave to our ancestor Nathanael Greene. It was a drum table from the original white house. Can anyone help me understand anything about my past ? My grandad died in the 50's and I wasn't born until 61. Any idea how I could backtrack my family ancestry? I'm guess Gen. Nat was a great x 8 Uncle. I'm 47 and would love to be able to research this. Thanks My dad's name was Jack Willis(born Greene) and he was born in 1924 to Karl Greene and LaVerne Warhurst.