I like you, but don’t go sticking your foot in your mouth. I’ve been programming for over 20 years and the thing that got me into it was image processing. I’ve written decoders for most of the formats discussed in this thread.
BMP has (and has always had) the very same RLE compression as TGA. (The only difference is TGA RLE can wrap lines, where BMP cannot.)
Further, PNG is lossless. That means that if you are getting strange stair-stepping effects there is either something wrong with your source image or with the PNG decoder. Now AFAIK, Blender uses the latest zlib png code base, so I don’t think there’s anything wrong with the decoder. Maybe your image processing software goofs when it encodes the PNG?
As you can also read in my above post, I like TGA. It is actually my favorite format. I’m not exactly bragging when I say that you are unlikely to find anyone else on this forum who knows more about it than I. The problem is that the people who bought TrueVision (Pinnacle Systems) act as if TGA doesn’t matter. Every TGA doc you will ever read traces back to a single, unofficial, “email” (this is before the days of email as we understand it now) posted by someone who looked in some ancient TrueVision hardware manual now lost and/or locked away in the vaults at Pinnacle and wrote a short exposition on how to use the easier parts of the specification.
However, the question is speed and size. FYI, size affects speed. With modern storage, it is unlikely you will see a significant difference between loading a TGA and loading and decoding a PNG. You will have to play with it to find out which works better on a specific computer. So, all things being equal, choose the format that uses less space on disk. People on dial-up connections will like you better.
And people who don’t like snot won’t have to put up with obnoxious, uninformed commentary.