I typically go with what is needed. If I know I'm not going to do any compositing, not going to fiddle around with post-production, I go with a regular good old PNG. If I am going to need a lot of wiggle room and I'm going to do post and color correction and I need all that data, I go with EXR 16 or 32. I don't tend to compromise, better save than sorry. With super extremely long render times of animation frames, I don't want to go into compositing only to find I cheapen out on the file output and now I have banding and not enough data to manipulate the images.
Zip and Piz are good and are supported by most industry software that support OpenEXR. It depends on your final resolution. For example at 16k, 8k, and 4K resolution the data that is lost isn't noticeable.(So say the experts. I haven't done the testing) When you start getting to 2k, 1k, UHD, and HD it becomes a little bit noticeable. The issue that I have with it is the additional overhead(More CPU usage) that is needed to decompress the DWAA and DWAB. So, basically it boils down to longer processing times in exchange for saved storage space. PNG in my opinion is a better option if you need to save storage space.
