I'm answering my own question to help others find all answers I struggled to find in one place. What above seems like a straight forward problem, actually presents multiple problems that I hope to answer sufficiently below.
Here goes.
Your WPF window that will serve as the generic dialog can look something like this:
<Window x:Class="Example.ModalDialogView"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:ex="clr-namespace:Example"
Title="{Binding Path=mDialogWindowTitle}"
ShowInTaskbar="False"
WindowStartupLocation="CenterOwner"
WindowStyle="SingleBorderWindow"
SizeToContent="WidthAndHeight"
ex:WindowCustomizer.CanMaximize="False"
ex:WindowCustomizer.CanMinimize="False"
>
<DockPanel Margin="3">
<StackPanel DockPanel.Dock="Bottom" Orientation="Horizontal" FlowDirection="RightToLeft">
<Button Content="Cancel" IsCancel="True" Margin="3"/>
<Button Content="OK" IsDefault="True" Margin="3" Click="Button_Click" />
</StackPanel>
<ContentPresenter Name="WindowContent" Content="{Binding}"/>
</DockPanel>
</Window>
Following MVVM, the right way to show a dialog is through a mediator. To use a mediator, you typically require some service locator as well. For mediator specific details, look here.
The solution I settled on involved implementing an IDialogService interface that is resolved through a simple static ServiceLocator. This excellent codeproject article has the details on that. Take note of this message in the article forum. This solution also solves the problem of discovering the owner window via the ViewModel instance.
Using this interface, you can call IDialogService.ShowDialog(ownerViewModel, dialogViewModel). For now, I'm calling this from the owner ViewModel, meaning I have hard references between my ViewModels. If you use aggregated events, you will probably call this from a conductor.
Setting the minimum size on the View that will eventually be displayed in the dialog doesn't automatically set the minimum size of the dialog. Also, since the logical tree in the dialog contains the ViewModel, you can't just bind to the WindowContent element's properties. This question has an answer with my solution.
The answer I mention above also includes code that centers the window on the owner.
Finally, disabling the minimize and maximize buttons is something WPF can't natively do. The most elegant solution IMHO is using this.