Q: Photo compression

Export them as a TIFF (an uncompressed image format) and use iTunes sync to transfer the TIFF to the IOS device

LN

select them in iPhoto and export (file menu ==> export) using Kind is TIFF as the export format

LN

I would warn you that Tiff is an uncompressed format and therefore the file sizes are huge. I wonder would high quality jpegs suffice. How will you be using these images? If it's only for showing then there's no point in having images that are higher quality than the screen you're showing them on.

Correct

BUT

The OP requested the "least amount of compression" and zero is less than a little hence instructions on doing an uncompressed image

with the least amount of compression?

Export them as a TIFF (an uncompressed image format)

LN

You'll need to know that if you export the files as TIFF files the file size will be increased by a factor of 10-15, i.e. a 1.5 MB file exports at 24 MB.  I doubt if your iOS devices will be able to hold those files.

Unless you plan to printing extremely large prints from those files you should not be concerned with additional JPEG compression.  These articles discuss jpeg compressors and image quality:

Does Saving a JPEG Multiple Times Reduce Image Quality

The Real Truth About JPEG images

How Bad is JPEG

If you export the photos as originals there will be no compression and you can then upload them to the iOS devices as already described.

Sure you're correct Larry, no question, but I was wondering why someone might want a tiff on an iOS device...