The New Family Member

[Joe_W]

I would guess it is a 7 speed freewheel not a cassette, judging from the overall appearance of the bike (unless it had been upgraded). Then the frame will have 127mm (or so) spacing in the rear (distance between drop outs). New road bike stuff is 130mm. This should in general work, though the rear dérailleur hanger will have to be adjusted (do that anyway). I have had luck with bending open the rear triangle (cold setting) on two steel frames of which one is abused as a cyclocross bike.
In general, if the "wobbles" are not too bad the wheel can be trued. It might have to have some spokes replaced (when nipples have corroded in place), but that's no big deal. The Vuelta wheelsets seem to be ok, I'd say that the 32 spoke wheelset is probably more durable if it has been built properly, that is the spoke tension is high enough and evenly distributed around the wheel. Hard (read: impossible) to tell if that's the case without having the wheels in my hand.
Oh, and bike weight is neglegible when compared to rider weight. Many of us used think otherwise (I guess) but then looked at the numbers (well, I did). Lighter wheels will make a difference though.