Well, I echo much of what has been said before - and of course cited in MDV's original post .
So it's picks, strings and guitar action / set up first for me. I also like to remove plastic nuts and cut myself a new bone one ( cosmetically 'aged' in cold tea of course ! ) Then , when my desired tone can first be attained with the guitar unplugged ; the cable is king. 'Cleartone' cable for clear tone with transparency and maximum articulation - or Monster 'Jazz' cable to silken and smooth things out . In the case of the later, I realise that what I am doing is adding a degree of sonic attenuation, but the 'jazz' cable is still the cheapest and most portable eq / mild compression 'effects' unit I own. :)
The best tone I get is with B.K.P's own heavy picks, especially when they have absorbed a bit of oil and the tip worn in. Strings being Thomastik 12, or 13 top Jazz Swing series Flatwounds.
When the action is set low and string tension nice and even across the neck, it makes me play more thoughfully and with more dexterity. This relaxed yet sure footed 'feel' , ensures I play to the requirements of the chosen genre - which is smoooooooooth ... 8)