meh, let's clear something up real quick. lossy compression is a compression format that cause a loss of quality in a graphic. lossless compression is a compression format that leaves the graphic intact (no quality loss).
JPG is a lossy compression graphic format, which means it uses approximate matches of repeated strings in order to compress the file, thus causing a loss in quaility from the original. However, this sort of compression allows for very small files, which is important for web use. I find an 80% JPG compression to be optimal, allowing the highest compressed quality, whilst providing a very small file size.
PNG is a lossless compression, although some programs allow you to impose a lossy compression, which further compresses the file, at a loss as above. There really is no reason to use lossy compression for PNG, and most people do not.
TIFF is a lossless format that usually leaves you with a huge file, not usable on the net, but is great for print. However, for print purposes, I convert everything to PDF, print standard, just to make sure the printers don't override and flip colors.
Other formats exist, of course, and while some are old (gif), others useless (bmp), there are still others useful for different purposes (stitch, etc). For the purposes of net use, GIF is still a valid format if your art has limited colors (256 or less). Converting vector graphics to GIF is recommended. PNG and GIF both allow for transparency, but PNG is better because of the lossless compression (again, this assumes the original graphic more than 256 colors).
For print, what matters most is pixel count per square inch. The higher the better, but too much and the printer will **** a brick, your graphic program will slow to a halt, and your newborn will have gone to college. More on this later.
