Webform Module or hook_form_alter() - What is right for me?
Webforms generally are best as contact/survey forms or some variant of them.

For an application like this, in my opinion it is just easier to implement your own form and do your own validation and submission. The validate handler could evaluate if the data is valid, and then the submit handler could create a new Node, set values, and save it.

Technically, you could do that submit Node creation handler with Webform, but it isn't as practical to me. Plus, if you haven't learned the Form API, this is a good opportunity to do so!

If this is Drupal 7, you could also take a look at Entity Forms and Rules, but again in my experience, getting to the goal is just faster with your own form or two and coding in what you want.