If I save it in JPG format with 100% quality, is this the best way to do it?
No … Yes, well … It depends.
(An edition added at the end)
Let's be a bit technical, but not a lot.
IrfanView uses a specific sub-type of JPG compression called 4: 2: 2, of lower quality than PhotoShop or PhotoPaint, which has a 4: 4: 4 aspect ratio.
So, if you started with a very high quality JPG image, you will lose information even with 100% quality settings.
The analysis is here.
Take an uncompressed image and place it on the already compressed one with a different mode of fusion.
Then use levels to increase the contrast of the image.
Here is a comparison between high quality and generic Irfanview (Gimp, PhotoPaint, Photoshop gives similar results)
If your image already contained 4: 2: 2 compression, compression blocks are already formed. Therefore, if you set this value to 100%, these blocks will probably be reused.
A problem here is that cropping up or to the left of the image may force the JPG algorithm to prepare new compression blocks over existing blocks.
If you do not mind and you can not see the difference, it's okay.
If your goal is to get a better compression ratio, you can compress it further. Try 90%. I would not consider an IrfanView editor as a "professional editor, just a casual one, so it does not matter.
One more thing … if it is for printing … why do you care about a heavier file?
You must try to maintain the overall quality. So, if it is for digital printing, use PNG. If the file was CMYK, use TIF.
IrfanView has a good quality compression. If you do not mind, the little loss of information, it is good. Especially for discontinuous crops.
Published a little later:
The Irfanview dialog box has a small checkbox to disable chrominance downsampling, then using a better quality algorithm. Similar to the ones I mentioned for Ps and PhotoPaint.