Thanks for all the info guys!
This is the guitar I have http://www.musiciansfriend.com/guitars/washburn-house-of-blues-electric-guitar-package. Cheap but gets the job done. It has 2 single coils and a double coil pickup.
I get the hum even with the guitar unplugged and with gain at 20.
With that guitar, if wired correctly at the factory, you should have no or minimal hum at switch positions 4 (mid and neck pups) and position 1 the humbucker at the bridge
With some guitars (not all) position 2 may give you the same result as position 4, only if the humbucker coils are a split wiring arrangement.
Anyway, before you continue further I would strongly suggest you try the guitar and cable plugged into a working amplifier (friend or shop) to ensure they are both working perfectly and noise free,
otherwise you will end up between ROCK and a hard place
i.e. that's THREE sources of possible hum and noise that you need to eliminate, starting with the guitar and cable
Once done you may find the amp build behaves better and that's all you have to concentrate on.
OTOH, if you like drama and frustration
please ignore the above