To combine and expand on several other answers:
Genealogy is the most broad categorization. It includes straight lines from grandparent to you, you to grandchildren, etcetera. But it also includes detours that go up and down generations like up to grandmother and then down to uncle and to cousins.
Lineage is everything in a 'direct line'. So it includes your grandparents (up, up), grandchildren (down, down), but not your uncle (up, up, down).
Ancestors are those who come before you. Anyone that comes before you (not sure if based on year or generation.) Your uncle is an ancestor.
Progenitor is a direct ancestor. A combination of ancestry and lineage. (grand)parents are in here, but your uncle isn't.
Descendants are all your offspring. This doesn include those who marry your offspring, but dóes include their children.
Successors is the best antonym to ancestors I can come up with. It's all that come after you, but no direct lineage requirement.
Household, Familia (Latin), Ménage (French) or Gezin(Dutch) are words that could be used for the conjugal family, i.e. a married couple and their children. But due to death, divorce, children going to live on their own, none of these are particularly precise.
Here's a more visual explanation, with thanks to the Hebblethwaites:
But what you really mean is a (sub)tree. It's that simple ;)