I got two male budgies about three weeks ago. One is about three months old, the other is about five months old. They are quite bonded to each other and quite sweet (adorable, to tell the truth). They will both eat millet out of my hand, and one is willing to climb onto my hand for long periods while eating. The other has also hopped on. But only to eat. I'd like to finger train them, with the point being for them to be out of the cage. So far, they've only been in the cage.
Is this the right procedure? Must I finger train them before allowing them out of the cage? That seems reasonable, but I'm a bit concerned we won't ever get to that point.

And on the subject of being out of the cage: their cage is in the main room I'm usually in -- which is a living room/kitchen combo with a stairway leading to the second floor. There is another a sitting room that seems safer to let them out in (at least at first). Is it recommended that I bring them in the sitting room first to let them fly around? Or will bringing them in there scare them?