In my opinion there’s no better option for managing renders in a pipeline than OpenEXR. I usually go with PNG over TIFF if I need a non-linear 16-bit image for whatever reason (which is almost never).
QuickTime files with the Animation codec are a decent option since they are lossless but they’re not particularly efficient when it comes to disk space since they are using RLE compression. QuickTime with ProRes 4444 is another good option if a little lossy compression is okay. If you don’t want to be tied down to QuickTime there are other lossless video codecs available like Huffyuv, Lagarith, FFV1, but QuickTime is going to be the most accessible for the average user and client.
Out of curiosity I just ran a test with a 123MB QuickTime file with the Animation codec. After going through 7-Zip with the defaults it’s down to 27MB (79% reduction in file size) and still lossless overall. So if you stick with QuickTime and the Animation codec maybe do further compression for archiving unless the underlying storage already does compression on the fly like ZFS does.