Best way to compress files and save on external drive?

Select the library in FCP and use File>Delete Generated Library Files. Remove all optimized, proxy, and render files. See how much the library and original media are then. You should not ever have to create these files looking at the type of video you're doing.

Do you mean that the exported file is that big? There are several different export options. Without seeing your video my guess is that you may be exporting as ProRes, which produces big files.

Select either Video and Audio, the H264. Or select Computer, which also yields a file with the H264 codec, but with mp4 format instead of mov. Both are great for putting online.

Please disregard my previous post. Tom’s answer, as usual, is the one you need.