UKC

Can people recommend me software for showing photos and video clips as part of a talk?

I'm not trying to use UKC instead of Google here. Searching for "slide show software" got me mini-apps for cycling through a bunch of photos automatically at home, while if I searched for "presentation software" or even "multimedia presentation software" I got Powerpoint-like programs better suited to text, graphs, etc.

What do people use now for their club slide show?

Well, something like catalog management application (like Lightroom, Darktable) often have reasonably good methods to produce photo collages/slideshows. That you can reasonably easily embed into normal PowerPoint presentation.

The LR/photoapp method is best to create a photo-slideshow/presentation, with minimal text/overlays.

For more information/text, PowerPoint or such with perhaps simply embedded slideshows might be the way to go.

The last resort, would be using a film editor (NLE), in which you can easily mix and match both photos, videos and even slideshow videos... and you also have the option to add text overlays etc. But it would simply be just "one" video... so if you wish to talk about a particular point, you need to pause the video. 

PowerPoint is fine for photo slideshow, just set up template slides, duplicate them, and copy your photos in. Although it can be a bit fiddly resizing the photos to fit nicely if you don't have them all in a standard format.

To be honest, I'd just use PowerPoint - importing photo album to picture-per-slide is quick and easy, the order of the pictures is easy to change just by dragging, and inserting videos to play automatically or on-click is equally simple.