Re: If you could have just ONE rig..
My JV Strat - Soon to have some new aftermarket pups and wooden pickguard. It's a keeper I think - plenty of mojo and it sounds great even with the stock tex-mex pickups.
Bogner Duende or Shiva combo - I was lusting after a Shiva, but the Duende is a more managable 18 watts, and it's more likely I'd be able to crank it to get some sweet tone.
Gibson Goldtop Les Paul - P90s, 'nuff said.
Pedals:
Vox Wah - with mods for two inductors and truebypass
Keely Java Boost - a very nice treble booster
Electro Harmonix Deluxe Memory Man - very nice sounding pedal, I spent almost an hour playing one at L&M.
Electro Harmonix Big Muff Pi or Double Muff - only played the BMP, but I'd like to try the double muff.
That's about it... I'm not really big on any other effects. Maybe a whammy pedal, but I'd likely use that more as a novelty than anything. Maybe a dedicated rackmount delay unit would be useful, but definetely not necessary for me.