Will a regular solid guitar cut it if I add other things like pedals/different strings/etc. or will only a hollow body guitar work?
Just turn the tone knob down.
Signature? What's a signature?

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Best theory lesson EVER!
tone nob on 1-2 and volume 4-5
Music is the holy grail, sod wine water and the blood of jesus
I've gigged with a strat a few times as a jazz player, and the other guitarist often gigs with his Les Paul. For the strat, it sounds much thinner so you have to compensate in volume a little, which thickens up the amp too. Both guitars sound thinner than a full out hollow or semi hollow but you can easily accommodate that by rolling off the volume knob to about 7 and the tone knob to about 4 or 5.

I find below that you lose clarity regardless of what guitar you are on.
An LP should work fine for jazz.
A strat, maybe. It will do a decent job, but it may not be that great.
Call me Wes.
Fender American Deluxe HSS Strat
Chicago Blues Box Roadhouse
Bad Cat Cougar 5
1957 Gibson GA-5
Ceriatone 18w TMB Combo
Hughes & Kettner Tube Factor
Various Ibanez TS9s
Weber MASS Attenuator
^^^ LPs were invented for jazz, the best way to get a jazz sound is mess with your tone knobs
my gear//
ESP Horizon Custom
Gibson LP Custom
Gibson V
Orange Rockverb 50
Mesa Triple Recti
Marshall JCM800 2210
also, try different pickups, the first LPs had P90s, so think about humbucker sized P90s
"A guitar is the human soul, speaking with just six strings..."- Eddie Lee

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