I would highly highly recommend against mixing a Portal Engine site and MVC site in Kentico (Web Forms and MVC in the same project). While yes, this is techncially possible (see this link on websites that use MVC partially in the portal engine on an older version of Kentico) it is no where near a best practice. There is a performance consideration (overhead of processing requests in both the web forms lifecycle and mvc pipeline), long term maintainablity consideration (hard to rememeber what goes / went where), and overall technical debt to deal with.
I would recommend jumping to MVC for the whole thing when it is time for a redesign as a best choice, or when your version of Kentico won't be supported by Kentico on Portal any longer (see the Kentico MVC transition guide)
If you absolutely need to do this in chunks, consider creating a second site in your Kentico instance at a different subdomain and learning MVC for Kentico there while still connected to he same instance. You could start treating the content as a content model accessible through the Kentico libraries nuget packages in a clean MVC architecture. This site could live at subdomain.website.com while your existing portal engine site could be at www.website.com. Again, this would not be my first choice, but it could possibly make sense in your scenario.