Tiff: (Tag Image File Format) is a common format for exchanging raster graphics(bitmap) images between application programs, including those used for scanner images. Tiffs are one of the best formats for composition within rendering. This is due to the lossless compression (so in other words you can get perfect quality like a bmp without losing any data) This makes it perfect for compositing your file. As you are not losing any quality to compression this does mean the file will render will require a large amount of memory compared to a .jpeg. We would advise only using this format on your final renders. Tiffs allow you to save multiple layers within the file also including an alpha channel.
EXR: is an OpenEXR Bitmap file. It’s an open source HDR (high-dynamic-range imaging). EXRs can provide high quality images, be comprised of lossless or lossy compression, support multiple layers, and hold a high luminance range and colour. This is a very similar format to the Tiff. A very useful advantage of the EXR is you can render multiple passes into a single EXR, making it even easier to composite.
Jpeg: is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable trade off between storage size and image quality. JPEG typically achieves 10:1 compression with little perceptible loss in image quality. As Jpeg provides this trade off between storage size and image quality it makes it perfect for test renders. If you are sending back and forth alterations with a client this would be the best format for the job.
PNG: (Portable Network Graphics) is a raster graphics file format that supports lossless data compression. PNG supports palette-based images and full-color non-palette-based RGB/RGBA images (with or without alpha channel). PNG was designed for transferring images across the Internet, not for professional print graphics and therefore does not support non-RGB colour spaces like CMYK. With transparent alpha capabilities and low compression PNGs are perfect for large animation frame ranges.
In our opinion these four outputs are the best for rendering. They should cover all the requirements for your project. Other file formats worth mentioning are BMP and TGA.
All of these outputs are renderable through RenderNow.