The ideal rack would be doubles to #3, a #4, and a standard passive set.
Like mentioned above to minimize weight you would likely need to tailor your rack to climbs you want to get on, because in my opinion both areas are fairly diverse as in you could be clipping a lot of bolts between a few gear placements, clipping nothing but bolts, or wishing you had a couple #4's and a #5.
You can get away with a standard single rack but doubles of 0.5" to 2" is nice. Mt Lemmon pro can be very awkward, I place a lot of stoppers and always bring my aliens. Like Bryanz said, there are plenty of sport and mixed climbs around, you can have a rad time with just a sport rack if you don't want to haul around your trad gear.