I subscribed fairly recently. At the time, I clicked on some download link. Later I saw in an email that offered three links, there were separate links for Photoshop and Creative Cloud. I would have clicked on only the Photoshop link, but I'd already initiated the download from an Adobe page. What I wonder is whether Photoshop will still work properly if I uninstall the Creative Cloud application.
I don't know why you were given three links. You only need to install the CC desktop app when you sign up, and then you install the individual applications you want from there.
The CC desktop app centralizes a lot of functions that would otherwise have to be part of each individual application. You do all install/uninstall/updates from the CC app, as well as access other resources like fonts and other things.
Make sure to uncheck all automatic updates. You'll be notified when updates are available.
And no, nothing will work if you uninstall the CC app.