System.Web.UI.Control is the base class for all ASP.Net Controls.
System.Web.UI.WebControls.WebControl inherits Control, and is the base class
for all ASP.Net WebControls. It contains a number of common properties and
methods that are used by all WebControls. You would inherit this class when
you want to employ some or all of those additional properties and methods.

System.Web.UI.WebControls.CompositeControl is the base class for all
WebControls that host other System.Web.UI.Controls. It is used when you want
to composite a number of Controls into a single Control. It is a container
which serves as the intermediary and coordinator of the Controls it
contains. It implements INamingContainer, which is an interface that ensures
that each Control has a unique ClientID, by combining their ID properties
with the INamingContainer Control in which they are hosted.

You probably want to create a CompositeControl. The following MSDN pages
should help with this:

http://msdn2.microsoft.com/en-us/library/zt27tfhy.aspx
http://msdn2.microsoft.com/en-us/library/3257x3ea.aspx