If you only want to expose a simple property in the viewmodel and handle the text for the choices in the view you can do a simple solution like this:
<ComboBox SelectedValuePath="Tag" SelectedValue="{Binding YourIntProperty, Mode=TwoWay}">
<ComboBoxItem Content="First choice" Tag="0"/>
<ComboBoxItem Content="Second choice" Tag="1"/>
<ComboBoxItem Content="Third choice" Tag="2"/>
</ComboBox>
Example with a bool property:
<ComboBox SelectedValuePath="Tag" SelectedValue="{Binding IsActive, Mode=TwoWay}">
<ComboBoxItem Content="No" Tag="False"/>
<ComboBoxItem Content="Yes" Tag="True"/>
</ComboBox>
Type-verbose alternatives (original examples)
Below are more verbose alternatives where the types are explicitly declared. Depending on your preferred style (or maybe some types that requires it), maybe it suits you better.
<ComboBox SelectedValuePath="Tag" SelectedValue="{Binding YourIntProperty, Mode=TwoWay}">
<ComboBoxItem Content="First choice">
<ComboBoxItem.Tag>
<sys:Int32>0</sys:Int32>
</ComboBoxItem.Tag>
</ComboBoxItem>
<ComboBoxItem Content="Second choice">
<ComboBoxItem.Tag>
<sys:Int32>1</sys:Int32>
</ComboBoxItem.Tag>
</ComboBoxItem>
<ComboBoxItem Content="Third choice">
<ComboBoxItem.Tag>
<sys:Int32>2</sys:Int32>
</ComboBoxItem.Tag>
</ComboBoxItem>
</ComboBox>
Example with a bool property:
<ComboBox SelectedValuePath="Tag" SelectedValue="{Binding IsActive, Mode=TwoWay}">
<ComboBoxItem Content="No">
<ComboBoxItem.Tag>
<sys:Boolean>False</sys:Boolean>
</ComboBoxItem.Tag>
</ComboBoxItem>
<ComboBoxItem Content="Yes">
<ComboBoxItem.Tag>
<sys:Boolean>True</sys:Boolean>
</ComboBoxItem.Tag>
</ComboBoxItem>
</ComboBox>
The sys namespace is declared as this:
xmlns:sys="clr-namespace:System;assembly=mscorlib"