One more thing is that (just as has been done on the OP's bike), an old bike with steel rims can be upgraded with an alloy rim front wheel to give safer braking in the rain.

Front wheels are so much more common to find at the co-ops than rear wheels, there really is a great surplus of them that can be had cheeeep(!).

Credit all of the low-spoke-count wheelsets that suffer rim fatigue cracks like clockwork at the rear driveside spoke nipples, and that leave an "orphan" wheel behind when the owner buy's a newer replacement wheelset. These will of course usually be 700c, but for errand riders it is not much of an issue and most bike's brakes can be easily adjusted 4mm down at the pads.