I use IrfanView for large images (large as in over 20Kx20K) as it handles them well, and sometimes when I need more than three instances of image viewers open at the same time.
Otherwise I personally don't like it, the options, controls, settings, interface etc, it's just not well done on the usability side critiquing as a former developer, none of them are perfect but damn IrfanView can annoy.
Also the two I listed offer portable versions without having to trust a third-party for such option, which is great for someone just wanting to check something out to see if they like it, and portable versions are generally the better option.
For editing beyond crop/rotate/invert/resize I'd rather use GIMP or Paint.net.
I just use PNG rather than BMP as it supports lossless compression so quality isn't an issue and has more features than BMP.
Unfortunately if converting images to JPG, even at 100% quality, some colours still suffer, blue and red being good/obvious examples, so quality is always a tradeoff with it.
One image format I remember being really interested in is
FLIF, haven't looked into it for I don't remember how long, but it seemed like it had a lot of potential especially for internet related things (which if I remember right Google was trying to do less impressively with their own image format, which unfortunately has a better chance of taking over being Google).