There are no right ways just ways that you understand.
Yeah tga is 8 bit fixed point only, iff is either 8 or 16 bit fixed point with 4 channels and a possible 5th 32bit float depth channel, tough very few programs can actually read that z channel since it contains NEGATIVE values (encoded in 1/-z distance; the direction is naturally negative in the fremebuffer. Good luck using photoshop to process negative values for example. And that means most artists will miss the entire concept on second 1).
Exr has a wide range of bit depth choices even such things as half float, which is at par with 16 bit fixed in size but contains potentially more data in the further ranges (larger space and more data in the near 0 area and data in over 1 area).
Anyway even with compression the deal is simple if you use full float you waste 4 bytes per channel, whith half float and 16 bit fixed you use 2 bytes and with 8 bits you use 1. So a full float image is going to be 2 times larger than corresponding 16 bit and again 2 times larger than the 8 bit.
Tiff is the format that everybody hates, because you can kill and entire manmoth of work with bad choice of tiff.
The biggest advantage of formats like tga is that its very easy to find applications that support the format, which brings in all kinds of tools into the picture, Also at the moment ist easier to find support for iff than exr, and its really hard to find very wide support for floating point pictures. Its not generally a showstopper but you'd be surprised what you can do with a farm of 20 machines that just happen to be sitting there and no licensing constraints and 10 lines of script glue. Not to be underestimated by a long shot.
PS: when you od gamma correction the difference between 16 bit and 32bit float is negligible, things change for depth fields and soem vector field operations tough..