Handling MVC Design With DatabaseDAO

I have done this a few times but I want to make sure I am doing it correctly. In other words creating a clean understandable program. Instead of posting code I will just talk about this is my plan:

Create a model (getter and setters)
Create a view (via swing)
Create a controller (pass the model and view in the parameter)

Database DatabaseConnection:
Use the singleton pattern

Database:
Create an interface called Database with all the queries I will need (insert, delete etc)
Create a class called DataBaseDAO and implement the interface database and get an instance of the DatabaseConnection.

Tying it all together:

In the controller should I use the "new" operator and create a new database class or extend the database class? I am thinking I should not do it in the controllers constructor but make a field if I use the "new" operator like:

private Database db = new Database();
Create a class called App
Create a new Model
Create a new View
Pass the view and model into the controllers parameter.

Am I on the right track? Is this messy? Is there a better way of doing it?