The template type popup is just a way of classifying the template you're about to make. It has no influence on your ability to make more templates.
When you say "it gives me that popup of template type but nothing else happens", I think this is where you're confused. Nothing else is supposed to happen after you close the popup. You're left with a blank area to write the source code for your template:
And there isn't a limit to the amount of templates a Wiki can have. As long as each template has a unique name, you can make more templates the same way you made your original template.