Cellar Door is right about the paper trail. Does your mother have relatives whom you can speak to? When did she arrive in the US? Did she become an American citizen? You can request her immigration file from the federal government using a Freedom of Information Act request, even if she did not naturalize. This will give information on her parents, birthplace, etc.
I'm researching my own mother's family history right now. I know a fair amount already, because my family is close and talks about the past a lot. But like most Americans, we have an immigration in our history, and searching old Italian records from America, especially when you know only ten words of Italian, isn't the easiest thing to do. I'm jealous as well of those British families who have been in the same place since William the Conqueror.

And yes, you will be the roots for your own child.

It might be a good idea for you to start documenting the pertinent details and stories of your own life, to give that gift to your child. Sometimes it's harder to do that as we get older and our memories get hazier.