I had a 1959 Gibson ES-330 (single P-90 model) that was easily encouraged to "on the edge of feedback" (and more if wanted). It was a full hollowbody thinline guitar. Man, the G string was magical, anywhere on that string and notes would bloom so nicely.
Next experiences are with full hollow ES-175 with Humbuckers and semi-hollow 335 and 339s: could easily feedback with high gain either from amp or turning up pedal, controllable by body movements like toward or away from amp.
The most "musical" feedback from my experience is the ES-330--So my vote goes to Hollowbody with P-90s.
The other way could be with a pedal made for that purpose, I've heard it mentioned before but can't remember the pedal--perhaps someone will chime in soon with that info.
Check out the just released new 330s (less money than a Vintage one--and hey, there's even one in our Emporium for like 600 less than a new one).
The Gibson blurb even mentions feedback potential:
More acoustic in nature than most electric guitars, the ES-330L provides a balanced voice with more power than other hollowbody guitars. The sum and difference of the top and back (not to mention rims) create a vibratory explosion of acoustical energy with an awesome midrange that exhibits a sweet spot at every fret. This results in its ability to produce musical feedback. The ES-330L starts feeding back at a lower volume threshold and delivers a wider dynamic range of musical feedback. Controlled feedback is musical and adds to the player's creative arsenal. With the ES-330L guitar, players need only pivot their stance a bit to get in the zone. Infinite sustain is yours at just the turn of your torso with overtones, undertones, howls, and shrieks at your beck-and-call. Because the ES-330L guitar starts feeding back at a lower volume threshold further from the source, you actually have a lot more control over the feedback."
And here's a feedback pedal (I've not used it so I have no idea how this one sounds):
It is amp specific too. My ES-335 into a Vicky 35115 tweed pro is like that. In a smaller room, at medium loud, you can get the notes to expand, then go over if desired. Quite controllable, really assists in phrasing.
Acoustic/electric would be 'best'. But that's subjective.
Big body ES type guitar.
IMO amps and pedals do more for this than the guitar. A certain amp can refuse to let the guitar 'sing'...but with the right amp (and pedals if necessary) many guitars cannot simply refuse...especially as you get louder.
A bassman with 3 tube screamers in front could make a sponge feedback....beautifully, I might add.