I stopped my search with VIK Slider: It worked out of the box, after a short period of puzzling about the unorthodox requirement to create a folder named "vikslider" to keep the images, instead of having the opportunity to assign just any deliberate folder (which would be the well established standard).
VIK Slider produces a nice, smooth transition from one picture to the next, and I will use it on this site.
I am giving not five but four stars due to the following problem: As far as I see, there is no opportunity to assign a deliberate folder keeping the pictures. Therefore, obviously, only one instance of the Module can be put in use on the site; it seems impossible to employ multiple copies of he module, each with its own folder keep the pictures. If one employs multiple copies of the module, they all would refer to the same "vikslider" folder...
A workaround might be to hack the php files of each copy and make it refer to a differently named folder. I have no tried, yet, but it shouldn't be too difficult.
Anyway, the lack of an option to choose the picture folder is a certain downside of this extension.
It's easy to set up, comes with a variety of cool effects built in and, most importantly, when I had a small issue and contacted the developers, they got back to me straight away with a solution.
If your looking for an Image Slider, stop here, you've found one!