I'd recommend using Qt Creator. Before I started with Qt development, I was also using Eclipse for a while, as well as Visual Studio. I tried to keep using these with Qt, but I ended up switching to Creator. It was weird at first, but once you get used to it, it's much better (especially for developing Qt applications).
With Qt Creator, you can develop standalone C++ applications that aren't using Qt. You have the choice of three build systems (that I know of): qmake, qbs and cmake.
As for developing big applications, many companies using Qt do so. Qt Creator itself (which is a massive project) is developed with Qt Creator. :)
A nice part about Creator is that a large portion of the development comes from third party contributors, so there's reassurance that it's easy to contribute patches for things you want to see added and/or fixed.
To get started, download it from here.