Best practice in IIS of redirect (wildcard) from one domain to another?

We are moving domains and servers. I have set up on new server (SSL).

I want to shut off old domain. I will get old domain pointed to new server.

Is it better in IIS to add the bindings on new server under the same IIS Site? Or is it better to create a new IIS site for and redirect it to the from there?

Another dimension in here is we could have links in both http and https but sites both require https. So one of the things I am worried about is redirecting and that it needs to redirect correctly to