Question about transformer design
For the power level you need, the transformer can be small, here is an example part (yours would be the smallest, datasheet here with dimensions):



You'll note it says 2 x 5V for the secondary, but you only have to use one of the secondary windings.  

For a switching supply, here is a small module that takes 85V-265V and outputs 5VDC, the dimensions are 26.7mm by 31.7mm:



Here is an example schematic, based on a teardown of the iPhone charger:



The above came from this site.