That will be because some trains through Sidcup/Eltham run a circular route out from London to Slade Green via Woolwich and then back in to London via either Sidcup or Eltham. The 18:37 >1 hour journey is an example of this. Obviously you wouldn't use that train to make a journey from London to Sidcup.
If you ignore trains that only go to Sidcup on the return journey, then as Antman says, it's roughly the same time from any of the main stations, so I'd just pick whichever station is most convenient for you to get to.
One other point - you're travelling in the rush hour so trains will be crowded. You'll be much more likely to get a seat if you go from Charing Cross or Cannon Street (not Waterloo East or London Bridge). (EDIT: And if at all possible I'd avoid London Bridge anyway - loads of rebuilding works there, and if you don't know your way around it might be harder to find your train).