Almost done the rebuild

Adjusting the gears on the Sturmey-Archer 3-Speed was actually kind of tricky because the frame didn't accept the cable sheathing.  Nevertheless, with a bit of tinkering I got things going.  I'll tape the handlebars, add a bell and a rack and that's it!
Here's a cost breakdown.
Peugeot bicycle - $7 (its the frame I was after but I also used the bottom bracket, cranks, rear rim, entire front wheel and the stem)
New tires - $15 (didn't get the fat ones yet)
New tubes - $5
Sturmey-Archer hub - $90
Spokes - $10
New bearings - free
Bell - $9.00 (struck me as expensive but it supports the LBS)

Since I had everything else in parts, didn't go with the new powder coat, and did the work myself the grand total of a fantastic bicycle for my daughter is $136.  You'd get a lot less bike for that around these parts so I think I did pretty well.

Pics of the final product next.