Simone,

upgrading from 9.9 to 9.11 should not be a problem if you regard DNN only. Anyway, there might be some third party extensions (skins/themes, modules...) that could cause problems.

Yes, 9.11 is the latest stable version, but there are some issues (e.g. UrlControl issue: cannot upload for any role (Only works for admin/Superuser) · Issue #5423 · dnnsoftware/Dnn.Platform (github.com)).

Best way to do is to make a copy of the website in a testing environment (web server and SQL database!), upgrade there and test everything. If you can live with the upgrade then apply it to the production server, but not before making a complete backup (just for the case...)

Happy DNNing!
Michael

Michael's advice is spot-on, as always.  In addition to this, upgrading/updating to support the most current versions of the .NET Framework is not required, but will be.  Regardless, it's a very low risk thing.  Latest versions of DNN require .NET 4.7.2, but installing and getting the Windows updates for version 4.8 is definitely the better way to go.  You might already have modules that require .NET 4.8.  

In general, if you have any uncertainties, doing a few test upgrades in a test environment should get you comfortable with the entire process.  Also, the process is usually at least a little bit unique from site to site.  So you'll want to take notes so you can repeat your own process.  

Here are a couple of resources to help you.  The first is a video of a presentation I gave at the DNN Summit conference (coming again this February) a while back, and the other is the slide deck from the same presentation.  

• Video: DNN Upgrades Made Simple
• Slides: DNN Upgrades Made Simple

Oh, and just to confirm for you, DNN Platform 9.11.0 is indeed stable, but 9.11.1 will be even better, of course.  It's coming very soon, but I wouldn't suggest you wait for it.  Upgrading from 9.11.0 to 9.11.1 will be very low-risk and easy to do.