Setting up and wiring guitars is dead-easy if you're handy with a soldering iron, can follow a wiring schematic and have at least some idea of what you're doing.
I used to get a lot of RF interference with my Dean, because it has some long lengths of wire in it that were not shielded. The pickups are wired to push-pull pots, and then the output from those go to the selector switch, which is in the upper bout of the guitar, like a
Les Paul, and then back to the output jack.
The Duncan pickup wires are nicely shielded, and the control cavity is already coated with graphite shielding paint and has an aluminum shield on the cover. But those long wires going up to the pickup selector (probably a couple of feet of wire total) were not shielded in any way.
A couple of feet of unshielded wire = one big antenna.
The noise and RF interference were intolerable at times, so i finally decided to rip out those long wires and replace them with 20- or 24-gauge shielded wire. It was hard to find... a few local Radio Shack stores did not carry any thin-gauge shielded wire for some reason, but i did eventually find a little electronic component shop that had some in stock. That did the trick. The guitar is eerily quiet now when i'm not playing.
Chances are, your Squier has little or no control cavity shielding, or your existing shielding is improperly grounded.
Upgrading your shielding is a good place to start. Shielding paint is good, but copper shielding tape is better. Put it inside the control cavities (around the
pickup cavities too, if you like) and on the underside of the pickguard. Solder a wire from the shielding to the ground. A good place to connect the universal ground is on the back of one of the control pots, then a single wire to the ground on the output jack. That should pretty much do the trick. Don't forget to shield inside the output jack cavity.
Since all of your wiring will be contained in the control cavity, you probably won't need to upgrade to any shielded wiring. I only had to resort to that because i had wires that extended out beyond the shielded control cavity.