A map might help to put all of the answers above into context:
http://oi68.tinypic.com/2vayqut.jpg
As you'll see, East Ham Underground Station is the closest, so the District Line from Victoria probably makes most sense. (Alternatively, if you're using the Thameslink service into London, rather than Southern, you can connect with the District Line at Blackfriars).
The closest National Rail station is actually Woodgrange Park but it's almost impossible to get to without using the Underground, so it makes little sense to aim for it.
Manor Park is almost impossible to access using only National Rail (or London Overground) routes but NJ's suggestion of using the Jubilee Line might be acceptable to you, as it's usually less crowded than many other Underground lines (and has modern, airy carriages). It all depends upon why you want to use only 'mainline' stations, rather than simply taking the Tube.