Ciao Filippo and welcome to these parts!
Feel free to Introduce yourself 
if you’d like 
There are many ways in which you could achieve that with Speckle, it all depends on the integration level, functionalities, and also appetite for coding that you have.
Here are some ideas on the top of my head:
Embedding the viewer
The lowest effort and quickest way is to use Speckle as it is and just embed the viewer on your website. Here are some links:
Using the viewer package
If you need more control over the viewer and its interactions, you can add it to your web app as a node package instead:
- @speckle/viewer - npm
- WORK IN PROGRESS API: Notion – The all-in-one workspace for your notes, tasks, wikis, and databases.
Custom everything
If you want to customize also the way data is uploaded/sent to Speckle, you can also fork our connectors and develop your own plugins/apps that do so instead. Or just use our nugets:
- GitHub - specklesystems/speckle-sharp: .NET SDK, Schema and Connectors: Revit, Rhino, Grasshopper, Dynamo, ETABS, AutoCAD, Civil3D & more.
- NuGet Gallery | Speckle.Core 2.15.2
I’d suggest experimenting and playing a bit with Speckle to see what’s the best avenue for your app. And whenever you have a question/doubt feel free to ping us!