Welcome to the forums.
Not to burst your bubble. But I can almost guarantee that the head gasket is blown, which will allow oil into the coolant or vice versa. These engines do not like hitting 120C, let alone staying there and driving. There was actually a design flaw in the original head gasket which makes them susceptible to blowing. I purchased my car with a new rad and blown head gasket, same story.
The car will be driveable with a new radiator alone, but your cooling system will be heavily contaminated within a few hundred miles. The head gasket job is a fairly involved repair, but not out of the reach of a DIY'er.