Frome tabletop prototype to a usable home device
If you have a relatively small number of parts that can fit on a board roughly the size of the Arduino you should consider using a prototyping shield like one of these: 
https://www.adafruit.com/products/51
http://www.sparkfun.com/products/7914

If you were making a dozen or more devices it might be worthwile making a custom printed circuit board, but for just one or two it is easier and cheaper to simply solder your parts onto one of these proto boards that then plugs into your Arduino just like any other shield.

For connecting your sensor, mount a jack onto the proto board so that your wire can plug into it.

As for your case, there are many commercially available cases custom made for Arduinos or you could make one yourself depending on budget and how fancy you want it to be. People have used Tupperware containers, wooden boxes, mint tins; the list is endless.