It's assumed that every web designer has had at least some training to understand which image format should be used in different cases, but many developers did not get this kind of training although they have to deal with images, too. So it's not a bad idea to give out a few pieces of advice.
Using PNG for maximum quality may be a bad idea
Some clients, with a limited understanding of how web works, ask for very high image quality and suggest to use PNG, since it's a lossless format. This is a very bad choice: saving in JPEG with a comparable quality produces significantly smaller files without a noticeable difference in quality. Always make tests and compare the results if superior image quality is asked for; you may easily save hundreds of kilobytes per image.
Don't be scared by SVG
SVG is a relatively recent addition, and it's also the most complicated graphical format to handle. That explains why not everyone uses it and, when dealing with a company's logo, the preferred choice is PNG. But using an SVG logo is certainly the best choice around for this kind of graphics. Logos usually are vector graphics: PNG converts it to a bitmap format, while SVG keeps it native. The vector version will be smaller and crisper at every resolution. Recently, SVG has added another point to its score: it's the ideal solution for retina displays. You don't need to have two versions of the same image, one normal and one for high-res displays, as with all other formats: one SVG will fit all.
Sometimes you simply don't have to optimize
Optimization is a word with a positive nuance, but when you optimize you lose something, and sometimes the compromise is simply unacceptable. When producing a full-screen background header image, it's best to make it very big so that it can cover most of the resolutions without scaling up too much. The common breakpoint for that is the typical 1920 x 1200 pixels of high-end displays, and most background images fit this resolution. Unfortunately, when dealing with larger screens, these images often fail to properly fit into the available space because the height of the header stays pretty much the same, while the width is considerably larger. In such a case you need a different background image with a proper ratio. It will be much larger than your original one and you will be probably scared by it's size (but if you use proper media queries, it will be rarely downloaded), but it's better than to show a misplaced header to some users (with high-end equipment).