Strings, I don't care what brand as long as they're tens. 9's are too flimsy, the tone suffers, and I don't dig fighting with 11's.
Purists can say what they want. With my Line6 Variax through my Line6 Pod, I can sound like anything I want. It's literally life-changing. The only thing better would be to have the sounds transferred directly from my brain to the recording.
However, that only goes for recording as managing all the sounds, levels and EQ crap live would be a nightmare.
For live, in my old band, I got the most amazing, distinctive tone with a Fender Strat Plus through a Peavey Mega Bass amp using one of those old Rat pedals for distortion and a Yamaha SPX-50 for effects.
However, in that band, the guitar was the biggest thing. I actively did not want the keyboard and rhythm guitar to be heard very much.
I would never go that route again.
Now, it's got to be a Gibson Les Paul or an SG. I've played every major brand that's around today and some that aren't, and nothing can touch the tone, power, definition, bite, and versatility of an old Gibson. Preferably an old one though. Les Pauls are kind of like Harley Davidsons. The old ones are monuments of design, quality and beauty. Now they're kind of like a xerox of a xerox of their former examples, trading heavily on the name alone.
But my old '74 Goldtop would kill you.
Amp-wise, I've never found one I could recommend enthusiastically.
There's a line6 amp that has a doubling emulator which I was thinking of getting, but I have yet to play through one.