How can I have an embedded website inside a windows app and also have it so that the windows app would startup the web server and go to the default page of the website?
Can I use the webdev server that comes with .NET framework? Or is there something better out there?
You can host full ASP.NET runtime inside pretty much any .NET application. See ApplicationHost:
To display a web page, you can drop a WebBrowser control onto your form, optionally provide an ObjectForScripting and you’re all set.