"Used digitally" is pretty broad, and depending on how they will be used or distributed might make a significant difference. As would the data type (vector or raster) shown in the map. For this answer, since your question title explicitly says PowerPoint and your body mentions that, that's what I'll address.
The first thing to determine is whether what you're exporting is going to be the entire slide or just a graphic on it. If you plan to crop out a small piece of a map and show it on a slide, you'll need a higher resolution export to do so.
Next, you consider the display resolution the PowerPoint will be viewed at. It used to be a pretty simple choice, but now you've got a variety of higher resolutions and aspect ratios available for monitors. Not quite so many with projectors. Pick an aspect ratio and understand the consequences (meaning if you use 16:9 and then show it on a 4:3, you're going to have black bars at top and bottom). With that ratio you can then target pixel dimensions for your slide (and map layout if they're going to be the same thing). My current 4:3 monitor is 1600x1200. So if I want to fill the screen, that's the pixel dimensions I would make my layout.
You can throw dpi into the mix here as well, which only matters for hardcopy output. Although if the program you're working in only allows you to set page sizes rather than pixel dimensions (Arc does allow pixel size specification), you need to work the math. At 150dpi, 1600x1200 pixels equates to 10.6x8 inches. However if I display that on a 4k monitor (3840x2160) two things are going to happen. First, because of the aspect ratio difference I'll have black bars on the sides. Second, because my image is less than half the resolution of the display, it might look blurry/pixelated if stretched to fit the screen, or really small if displayed at 1:1.
So the bottom line is, pick a reasonable pixel dimension to use to balance the increased file sizes of larger resolution with the maximum capabilities of your targeted displays.
Choice of format comes down to what the map is of, what you're importing it into, and balancing out loss of quality to compression. PowerPoint can handle a variety of formats. While it's true vector pdfs would allow you to scale without loss of quality, you're targeting a specific resolution in a presentation anyway, so you won't really be scaling or zooming in to anything on that end (zooming/scaling should be done on the Arc end of things with a new image exported at the right size). Tif just gives you lossless quality when saving and resaving, which is mostly for again resizing things or editing. There's no reason not to just use jpgs at an appropriate size/resolution. You might use bmps or pngs if the color palette of the map is really simple. For a PowerPoint, the key is going to be keeping file sizes to a minimum so the presentation stays small, manageable, and responsive in playback.