Summary:
JPG does not support transparency. InDesign can detect white edges with Object>Clipping Path Options, Detect Edges
Does not support layers and is a lossy format (image degradation – https://qualityinprint.blogspot…..acts.html)
TIFF and PSD support transparency, fine for wholely raster files, as tiff and psd only output as raster. So any text or other vectors converted to the native resolution of the Photoshop file (found under Image>Image size)
Supports layers.
PDF all the things that TIFF and PSD do except that it can output Vectors and Raster, so text and vector shape and vector masks are retained as vector on output. Great for a file with both raster and vector content.
Again – supports layers
EPS from Photoshop – Does not support layers. However, it does output raster and vector. BUT, once you open a photoshop EPS to edit it, Photoshop by nature, rasterises the file. Layers are not retained. If you do use EPS from Photoshop make sure you make a LAyered PSD or TIFF or PDF version (if you're saving to these just place them in InDesign anyway – however, Quard doesn't play nicely with pdfs as far as I know, so you may have to use an EPS for Quark, do make sure you have a layered version in the native Photoshop format (PSD).
And there may be issues with colour management with EPS? I'm not an expert on colour management with EPS so I can't really go further with that explanation.
In regards to PNG files – yes they can be used in InDesign, but I would not. PNG is a Portable Network Graphic designed for the Internet. It has a RGB profile (although it can embed an ICC profile) it's not really ideal for placing into InDesign. Try to avoid PNGs if you can.