I assume you're in Az, so you shouldn't have to worry about carrying rain gear, unlike those of us in the Pacific Northwet.
(*sigh* I really miss biking in Az.)
I use
this bag for my (almost) daily commute (there's a similar one for mesh seats), and I can
just cram a change of clothes in there with my rain gear (when I'm not wearing it). I leave an extra pair of shoes at work so I can ride with my clipless pedals. You might have to hang your water bladder separately. I'd get a smaller frame pack, like one of
these for your tire pump and repair kit. The nicest thing, IMO, about the seat back style bags is that they are easy to take off and carry with you, and put back on the bike.
Having said all that, the bag is a bit too small to carry rain gear, a change of clothes, and anything like lunch (unless it's just a couple power bars), so I'm in the process of fitting mine with a rear rack, and hoping I can find my panniers (just recently moved, everything's in boxes....).