We have had Punto's for 15 odd years, great little cars, go well, ours are the Selecta, the auto box, for the wife.
Our latest one is a Dynamic 1.2 16v goes very well, no probs with it. Just done the cam belts, found the water pump was leaking. Only issues I have heard is the cylinder head gasket, but like the K series dont have much coolant. So any loss will make the gasket go.
Easy job on the Fiat, think your's would be due, but Google Belt change periods. Check the exhaust, replaced ours, then just normal stuff, tyres, pads etc.
Only other thing that we have replaced was a sender for the oil pressure as that was flashing up a warning of low oil pressure.
We would have another, surprisingly roomy inside.
Good luck if you get it.