If I were in your shoes with your needs here's exactly what I would use:
Guitars-you already have them covered, Strat and Les Paul
Amp(s)- some of the best all around amps ever: Fender Super Reverb, Dr. Z Maz 18 (hell any Z with enough watts for your needs would be awesome), or the formentioned Bluesbreaker JTM45. I would say that my Z is my desert island amp right now, it just sounds amazing and Fendery with a Strat and like an old Vox/Marshall hybrid with humbuckers.
Pedals- Of course this depends on what amp you went with, but the guys above are right. You need a great fundimental tone be it mostly clean or mildly distorted. All of the amps I mentioned do that semi clean mild breakup thing great that sounds much more lively than say a sqeaky clean Fender Twin. I like my cleans with a little gainey warmth. Anyways, here's my desert island pedal pedal suggestions: Fulltone Fulldrive II, Fulltone Catalyst (for fuzzes), Vox wah, a tuner (I use the Planet Waves ones), Boss DD-3 or Line 6 DL4 for delay, and that's about it.
You should be able to cover a lot of ground with a killer single coil guitar, killer humbucking guitar, a nice combo amp, a couple gain boxes, a wah, and delay. Sounds like a lot, but it's what works for me .
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.