Safety with '50 Lionel

Jeremy723, when you move the handle and power goes to the track yes, the posts are "hot" or live and the track is also. If I'm understanding your question. In a typical track setup the middle rail is positive and the two outside rais go to ground.

If you get a shock there really isnt any danger. You can lay your hands directly across all three rails and you typically will not get shocked. I would not be concerned of any danger to children and dogs.

There is no danger from the output voltage from the transformer.  If your hands are wet and you touch both rails, you might feel a the voltage, but not enough power to get hurt.  However, this old equipment was made to lower safety standards than are used today. Additionally the equipment is 50 years old and the insulation may be deteriorating. I recommend plugging old toy train transformers into outlets that are protected with a GFI.  That way if a problem did develop everyone would be protected.  The other issue is that the circuit protection in the old transformers was not very good and has gotten worse with time.  It would be good to put a circuit breaker on the output of the transformer, maybe 5 amps, to protect from overload.  The last thing is that you should never leave the room with the transformer plugged in.  Never can tell what might happen when you are not there. I use a power strips with a switch in it to shut everything off when I leave the room.  There have been lots of posts on this subject and there are several web sites that cover this topic.  I would suggest you use the search function to find more details.