Vibro-King Sound & Settings
I play an ES-346 (stock '57 Classic pickups) through a VK and have no problem getting everything from a clean, swirly "acoustic-like" sound to a growly horn-like overdrive to a powerful crunch.
I have my neck PU set way down - slightly below the mounting ring on the bass side and about even on the treble side. The bridge PU is a little higher (adjusted by ear to match the output of the neck pickup) and is also set lower on the bass side and higher on the treble side.
I use a custom-guage "heavy-top/light-bottom" string set: 9.5, 13, 18W, 24, 32, 44. (I buy five or ten sets at a time from a small local shop, and get a good discount on the price.)
The guitar setup is important, as it helps to keep the bass from being too prominent. I did this long before acquiring the VK; it helps with all of my amps.
Run both guitar volume controls at around 7 and select both pickups. If the sound is shrill, roll back the tone on the bridge pickup. If the sound is thin, cut the volume of the bridge pickup or bring up the volume of the neck pickup.
Getting a good clean sound is the best place to start. It's easy to get distortion. Yes, the VK will break up early. However, it's the midrange frequencies that most influence the breakup. Run the mid control all the way off, bring the treble up about halfway, and bring up the bass enough to give you a nice full, balanced tone. If your preferences run more to tweed than blackface, bring the treble down and the mids up until it sounds right to you.
Keep the amp volume fairly low - three or four is about as far you'll be able to push it with a humbucker guitar without getting gritty. If you need more clean volume, raise all of the tone controls, not the volume! (Trust me, that's the way the amp is designed...)
A light touch on the strings is very important to getting a clean tone. (The nice thing about developing a lighter touch is that you can then dig in for solos without ever having to touch a switch or knob of any kind.)
If you have a hard time cleaning up the sound by touch, try plugging the guitar into input 2 - that'll give you a bit more headroom. It'll also cut some of the highs from the guitar, but you can get that back by raising the treble on the amp or the tone and volume on the bridge pickup.
Obviously, if you want more distortion - dig in! Even more? Bring up the mids. Still more? There's plenty of room on the volume control... The really nice thing about a stock VK is that the alnico-magnet speakers are less efficient than the ceramic-magnet speakers in most amps, so you can push the amp harder without getting (too far) into hearing-damage territory. (Always wear earplugs when you crank the VK.)
Finally, make sure you've got a decent low-capacitance cord going straight from the guitar to the amp. The Horizon cables are good, as are the Carver-made Fender USA Instrument cables.