There are two main sources of electrical hum and buzz in electric guitar systems, and both enter through the pickups and electronics. The sources are AC electrostatic fields and alternating electromagnetic fields radiated from electric wires, lighting dimmers, fluorescent light ballasts, power transformers in amplifiers et cetera.
Pickup coils and unshielded wiring in guitars act as very effective antennae that capture these radiated fields and pass the unwanted hum on along with the guitar signal.
Historically Fender's Standard Single Coils can be quite noisy and if you are using pc recording software there will likely be reactive IF between the guitar pick-ups, your amp and your pc monitor as, especially if you are working in a small environment e.g bedroom (and more especially if it has light-dimming switches!).
Fender do still produce a Vintage Noiseless pick-up which will reduce the horrible buzz significantly.
I'm not sure changing the pick-up selector will do much, unless it's faulty of course.
One little tip that I have used is to line the pick-up cavities and jack socket chamber with silver foil (making sure of course that there is no contact with cables) which does help reduce IF.
Other than this, make sure all your contacts are sound and clean.
Hope this helps
JTB