I'd get a custom made 24 fret Les Paul with an extra long neck tenon and no heel, with a zero fret. Korina body and neck, with an even flamed Maple cap and Ebony fingerboard. Oiled neck and no fret inlays. except at the 12th fret.
As for amps...well...maybe a Fender Twin for clean and a JCM 800 for dirty with and extra pre-amp tube of two for some more gain...but both modded with graphic EQs.
Palmer PDI 03 speaker simulator a splitter, sending one side to a roland tape echo, and one to a delay pedal...into a stero hi-fi power amp like the HH V800...
Oh wel...you did say
dream rig...
Oh yeah, and an RMC3 Wah. And George L cables.