The spring on the switch can be on either side (there's no difference, electronically). The string ground on your tele is usually made by the metal baseplate under the bridge pickup in contact with the metal bridge. But if your pickup doesn't have a metal baseplate (some don't), run a ground wire from the back of the volume pot to the underside of the bridge (see the dotted line).

For short connections between components, use standard non-shielded wire. Typically, white wire is used for hot and black for ground. For vintage-look wiring use cloth-covered wire. However, if you want to reduce unwanted electrical noise you can use shielded coaxial cable for the connection between the controls and the output jack.