Out of Pod Experience

Bitmaps are the largest size. Generally when I want to load an image onto imageshack I convert it over to Jpeg for compression and put it up that way.

To me, as a amateur photo-shopper, I find PNG and JPEG to be about the same size. The difference is though is that png doesn't give me a white background with the image, it'll only show what you created. As an example, when I was making sigs for the Rift forums I would put in my character and generally a simple bar stretching out from his waist which usually had a quote, then I would stick his name on it's own in a corner. When it shows up in the forums my 'background' would be whatever color the forums was so it is kind of like he is sticking out so to speak.'

Now I haven't a clue what these environment Maps and bump maps are, but I'm guessing that png is going to be what you want. I happen to know that Minecraft skins are also created for PNG so it may be the best solution for modification in your case.

Fake Edit: Looking at one of my sigs made in both formats, JPG has the smallest compression with PNG being double. But the images are 53kb and 102kb, whereas a bitmap (pick a game screenshot) is about 5 megs.

What that is called is an "alpha channel", which is a very powerful and useful thing in CGI. Think of if like an extra channel that indicates what part of an image is invisible or not, or partially see through areas of your image etc. So if you want a white background with .png, then fill it with white paint, done. Don't just leave it blank. For high end graphics this is how we can composite images over other images and have them nicely blend together so to speak.

In comparison, neither .bmp or .jpg are capable of having an integrated alpha channel, thus are severely limited for high end CGI.

size:
.bmp most data --worst
.png very small data --best
.jpg smallest data (depending on the quality setting) --best

quality:
.bmp highest quality ie. no image compression. --best
.png ALSO highest quality ie. lossless compression. --best
.jpg terrible quality (depending on quality setting) --worst

YES, both .jpg and .png can be used for 3D mapping, it really depends on the software you are using and if they accept it, but I have not heard of any professional software not able to 3D map with either of those options.
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--> For any type of digital project, 2D or 3D I would recommend using .png if you can. It is a very widespread industry standard, highest quality, lossless compression with very low data size, PLUS ability to use an alpha channel, and no odd variants to cause cross platform incompatability. It is just about the perfect digital image format for general 3D work.


Some other formats:
.tiff not as small data as .png, and not as widely supported by various professional programs.
.tga not as small as png, does support alpha channel but there are oddball tga variants that have compatabilty issues cross platform.

I'm probably am not the most qualified to answer that question in this regard (even though IQ is what I do for a living). In most of my instances my quality is only as good as the images that I download. I know with png you have a lot more options in exporting when you save the file so I am gonna go out on a limb and point at png in that respect. I'll be taking PS either next quarter or the one after so by then I could have some more answers.

Here is a screenshot that I have which we can use. I had it on imageshack as JPG (was converted from bmp. I downloaded it, converted it to PNG, and re-uploaded. Chances are we'll only see the quality of JPEG on both but maybe you'll notice a difference.

JPG

PNG