This may be an obvious question, but I think there may well be multiple ways to implement it, so not only will this be useful to me, hopefully it will be useful to others.>
Just specifying DataTemplates in the Resources with the respective DataType is enough, e.g.

(Note that DataTemplate.DataType can also be used for implicit XML data templating (see docs), the property type for that reason is not System.Type, so unlike in Style.TargetType you have to use x:Type to reference a CLR-type. If you just enter a string it will not be converted to a type.)
You might also want to look into CompositeCollections, to get clean merged lists of varying types.
Sample data i used:
ObservableCollection data = new ObservableCollection(new Employee[]
{
new Employee("Hans", "Programmer") ,
new Employee("Elister", "Programmer") ,
new Employee("Steve", "GUI Designer") ,
new Employee("Stephen", "GUI Designer") ,
new Employee("Joe", "Coffee Getter") ,
new Employee("Julien", "Programmer") ,
new Employee("John", "Coffee Getter") ,
});
ObservableCollection data2 = new ObservableCollection(new Machine[]
{
new Machine("XI2", String.Empty),
new Machine("MK2-xx", String.Empty),
new Machine("A2-B16", String.Empty),
});
CompositeCollection cc1 = new CompositeCollection();
cc1.Add(new CollectionContainer() { Collection = data });
cc1.Add(new CollectionContainer() { Collection = data2 });
Data = cc1;