Image Formats
Note: Cheetah 3D 8.1.1 also supports OpenEXR (.exr) images, e.g. for HDRI lighting (manual: HDRI Light; Third-Party Libraries), not yet covered here.
In a nutshell, the most important file formats to know about are PSD, PNG, JPG, and if you need to deal with 16 bpp images, TIFF, HDR, DNG, and proprietary RAW formats such as NEF (Nikon) and CR2 (Canon). You may also encounter TGA ("Targa") files, especially when dealing with high-end software (there's nothing magical about TGA, it just happens to have been a file format used by a lot of 3D packages back in the days when 3D meant spending as much on your computer as you would on a new Honda Civic).
File Size
Uncompressed image files tend to be huge — a typical 24- or 32-bit image takes up to 4 bytes per pixel, so a 1024x768 image is 3MB uncompressed (or more when you include metadata). Most TIFF files are uncompressed, so unless you need more than 32-bit deep images, avoid TIFF.
RAW images, produced by some cameras, are an unusual case, these store unprocessed sensor data, generally in the form of grids of red, green, and blue pixel data with 12 or more bits per pixel. Processing RAW images into something recognizable as a picture involves synthesizing RGB pixels (one for each red, green, or blue source pixel) by interpolating color values from adjacent pixels, which in turn requires a knowledge of the structure of the camera's Bayer filter.
RAW files are usually compressed, sometimes lossily and sometimes losslessly. A typical RAW image file from a 16 megapixel camera might be 10-15MB, which is a lot, but significantly less than the uncompressed size (which would be 24MB for 12-bit RAW).
Bit Depth
Bit depth refers to how much color information is retained for each pixel in an image. The standard options are 8-bit (for standard monochrome images), 24-bit for RGB color with 16M or so different colors, 32-bit for 24-bit RGB with an 8-bit alpha (transparency) channel, and bigger numbers for images with more color detail or dynamic range (there are a lot of possibilities here, so I won’t go through them all). HDR (high dynamic range) generally refers to 48-bit or even deeper image files.
Lossy or Lossless
Uncompressed images contain all the image data you started with, but so do losslessly compressed images, of which PNG is the most flexible and widely supported. PNG is great because most images will be significantly smaller than if they were uncompressed and it supports alpha channels. (PNG also supports 8-bit "indexed color" and other bit depths.)
Most images can be lossily compressed with little or no visible deterioration (“artifacts”). The most common and popular lossy compression format for images is JPEG. The important thing to know about lossy compression is whether it’s intended for production or delivery.
Production or Delivery
Most file formats were designed with at least one purpose in mind. E.g. PSD files are designed for production — they’re not easy to read or easy for third parties to support, they’re not a “standard format”, you can’t view them in a typical web browser, and they’re big. But they can preserve huge amounts of data useful for someone trying to edit them, including layers, editable text, vectors, and so forth.
Lossy compression that is intended for delivery tends to get a lot of mileage (i.e. file size reduction) from throwing away data that people won’t perceive. E.g. human beings are much worse at distinguishing shades of blue from shades of green, so JPEG throws away subtle shifts of blue colors more quickly than it does greens. Similarly, humans aren’t good at differentiating dark colors, so JPEG throws away information in darker areas of pictures before it throws away information in light areas. As a consequence, it’s a bad idea to use images that have been lossily compressed in a manner intended for delivery (i.e. end users) for production. (Imagine if you are scanning in negatives and storing them as JPEGs — the JPEG algorithm will throw away the most important data first because light areas will be dark and yellow areas will be blue.)
In a nutshell: use PNGs for textures when possible. If you must use JPEGs, use high quality JPEGs.
Alpha Channel Support
Some image formats, such as PNG and TIFF, support alpha channels (transparency) and others do not. Don’t save images where transparency is important (e.g. where you’re planning to composite the resulting images) in the wrong format.