I have a form like this
If you don't use ajax, the form will be submitted, and the browser redirected to the action url of the form. The only way to do a redirection after the submit, is to do it in the handler of the action form. You could however add a parameter with the URL you want to redirect to.
The only advantage of that solution over a solution involving ajax is that no javascript is required. It would work whether javascrit is enabled or not.