Best way to display a long form with many dynamic questions

Question

I need to make a form with about 10 different inputs in it. Normally, I would put this on a single page and have the user scroll down. This seems like the easiest way to do it most of the time. But in this form, I need to user to perform a number of things.

I need them to:

1. Choose between three options of a single product.

First here is some information on the products option 1: the base product itself option 2: an addon to the base product option 3: both the base product and the addon

2. Ask them to login
3. If option 2 - user selects which product from option 1 to attach their purchase to.
4. all 3 options have different forms that need to be done.

What would be the best way to display this information? As far as I can see, I can only see these options.

1. 3 separate forms
2. 1 long form with elements that hide and show based on what radio buttons they choose for products - not sure how they would log in
3. 1 multi step form with different "screens" showing up depending on what the user selects.

What do you think is the best way to display this?