The best file format to store such large images depends on your goal.

Is storage space efficiency the priority?  Or image fidelity?  Is the image expected to be edited or converted to other formats in the future?  Are compatibility and portability a concern? Is the image of a high bit depth and needed to preserve this for use on high fidelity displays or printings?  Or is a balance of some or all of these required?

Although there are lossless compression techniques that achieve some small size improvement without image degradation, compression beyond this is always a tradeoff between file size and image quality.  They can even have tradeoffs further afield.  

For example, some modern lossy compression techniques, like that which is used in the JPEG format, aim to appear lossless to the eye by leveraging idiosyncrasies in the way the human eye and brain perceive images.  This can lead to substantial file size improvements while appearing to retain most or all of their quality when viewed in typical ways by humans on a typical display.  However, if zoomed or printed very large (such as a poster or billboard), the compression artifacts can become very visible and distracting.  

Complicating matters further, these artifacts--and the loss of image information from the compression--are also not invisible to machines.  Just like a photocopy of a photocopy of a photocopy, or a picture of a picture of a picture, highly compressed images can introduce even further loss of fidelity if edited, and more each time if edited repeatedly.

For these reasons, JPEG is a preferred format for webpages, but not by graphic designers and archivists, as a continuation of our example.  Webpages benefit from the increased loading speed of small file sizes and web images aren't typically enlarged drastically or expected to cater to high fidelity editing.  Archivists, on the other hand, wish to preserve as much image fidelity and compatibility as possible.  And graphic designers need to be able to edit, display, and print images at professional quality and large sizes, and typically work on pro systems and software that can support any file size necessary to get the job done.

Thus, as you can see, the decision of format (and settings, for formats like JPEG that offer them) is best made taking into account the use cases.

I can walk you through determining the best format for your use case, or, if you have many use cases, I can give you an overview of each format and its tradeoffs and typical uses.  Which would you like to do?
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