I kinda take 'beaming' literally in that your molecules and that are transported down some kind of 'corridor' and reassembled at the other end.
Maybe in the original series, but apparently not in TNG
. Two episodes spring to mind, though I can't name them:
One where Picard beams out into an energy cloud or something, having been possessed by an alien entity. If I remember correctly, no Picard rematerialises at the other end, as the entity is of pure energy and wishes to remain so. Picard is then re-assembled using the Picard pattern held in the transporter.
The other is the "two Rikers" episode from season six. Riker asks which is the original and is told that they both are because they were materialised from the same patterns.
As regards the "copy" issue, the current prevailing view of how teleprtation would work is probably in line with what current quantum teleportation experiments have shown; that there's no meaningful distinction between teleporting the quantum state of an object and altering its location; ie when it comes down to the nuts and botls of the universe, nothing is nexessarily destroyed.