Sounds like you've got a really fun project and like most Tableau users, see the value in giving your audience the ability to interact and make their own discoveries.
Fortunately Tableau has three different solutions for people to use when wanting to put Tableau visuals out onto the web - Tableau Server, Tableau Public and Tableau Digital. Which solution is the right one for this project depends on a couple things like how much security you need around who sees the published visuals, who can access the underlying data and how important it is that the data reside on premise vs. in a secure cloud, etc.
I definitely recommend you talk with your account manager since they can help you narrow down the right solution based on your specific project needs, however here is a quick reference of each of the three solutions:
1. Tableau Public - Free solution that allows users to publish their work up to the Tableau cloud and let everyone see both the visualization as well as access the underlying data. Tableau Public Link.
2. Tableau Digital - Upgraded version of Tableau Public that allows for a subscribed user to disable access to the underlying data of a published visual while maintaining the ability for it to be seen by the public. Requires Tableau Desktop Professional. Tableau Digital Link.
3. Tableau Server - Server software that you install on your own web servers and allows you to keep your data onsite. Gives the ability to password protect visualizations or make them open to the public. Requires Tableau Desktop Professional. Tabeleau Server Link.
Hope that helps.