so I’m working on this project currently myself, so I don’t have all the answers, but from my understanding, generating the quotes, and being able to share them on twitter are two seperate areas.
you’ll want to find an api (think of it as a database of quotes). for starters, checkout this website, see if you like it
Next, once you have your website up and running, you’ll want a twitter button to let your users easily share the content. get started with this website
hope that helps