How can I create a second variant based off the first variant choice?

What you’re referring to is “conditional logic” – which isn’t something you can do with the built-in settings. You’d need a “custom product options” app to be able to only show specific options, based on the first set of choices.

https://apps.shopify.com/search?q=custom%20product%20options

So you would need one of the apps from the above link, and then you would make all of your options/variants through the app.