If you will not always download all files from the archive, TAR / GZ may not be a good idea, because you cannot extract specific files as needed. For this reason, many games use ZIP archives that allow you to extract individual files as needed (a good example is Quake, whose PK3 files are nothing but ZIP files with a different extension).
Minizip , which is a ZIP library built on top of zlib, picked up a bit of search . I could not find any separate documentation for myself, but the header files seem to contain a lot of comments, and I believe that you can handle it.