Originally Posted by: GramboI'm not sure that a 250Kohm pot has enough resistance to completely silence the Guitar.

I know that single coil pick ups use 500Kohm pots - Strats.... etc
And double coil pick ups use 1000Kohm ( 1 megohm )
You might find a diagram @GuitarNuts.com
As for the hum - putting the strings on wouldn't help - but some metal component ( I suspect a pot body ) is not grounded

250k pots are used on single coils.....500k pots are used on humbuckers....25k pots are used on active pickups..... any one can be used for the either... but usually to get the desired tone thats the way they're applied.

The hum could be a series of things if you didn't go from an existing schematic... check the grounds as mentioned... and check out a Tele schematic like someone said. that wouldn't be a bad idea at all. it should be a pretty basic setup