It looks like it's in great shape! I'd probably install new cabes and housing (brake) just for safe measure. You'd be amazed at how much better your shifting and braking will be with new teflon cabl housing compared to the old stuff.

It will probably take 700c rims, you just need to be able to extend your brake pads another 4 mm to reach them....easy to measure or eyeball. It looks like you *might have that with those brakes (hard to tell from here).

If not, I'd personally install the 700's anyway and just find another set of brakes (at your co-op) that will work....probably tons of old road brakes there.