PNG

PNG seems to represent the best option for space/quality ratio. If you have a good image creation suite, avoid Adam 7 interlacing, just because it loads somewhat slower.

I would say it depends on the image. Since I'm going to assume "game loading time" means downloading time, you'll want to reduce each picture's file size as much as possible.

Different formats are intended for different images and uses. PNG is great for simple images with a low to fair number of colors, and is lossless. However, if you're dealing with an image with tons of colors or gradients, such as a photo or texture (since you mentioned interface images), JPG can give you decent lossy quality in a small package. For smaller images with very few colors, an indexed GIF can be surprisingly small.

BMP should only be used when processing speed is a major concern or when you don't have the resources required to load more complex formats (the windows XP boot image is stored as a BMP, for example). It should almost never be used in BYOND (unless the image is tiny, like 4x4)

PNG uses transparency(Also great quality, GIF is mainly used for animation... still trying to work out a purpose for JPG :)

JPEG is good for some images, like pictures (most pictures are JPEG), as its pretty small but still kind of lossy. PNG is better for artificial images; its lossless and still relatively small.

PNG is the best though ;)

Ping .PNG is the best.