From JPG, PNG, BMP and TIF, only JPG introduces a lossy compression and can achieve the lowest file sizes. JPEG is a standard created for photos, so it'll perform very well on any sort of pictures or anything with smooth gradients.
For text, however, JPEG will introduce so-called ringing artifacts. This is because high frequency information is removed in the compression stage, after the image is transformed from the space into the frequency domain. Simply put: You cannot reproduce the sharp edges of text, or any sort of graphics. This effect can be seen in the following picture:
If you don't care about the quality, simply save your scans as JPEG images. Set the quality range depending on how large you'd like your documents to be. The ringing artifacts disappear with a high enough quality setting, e.g. 85 on a scale of 100, but they will be noticeable once you zoom in.
All the other formats apply lossless compression, so they will be larger, but you won't get any quality degradation. Taking that into account, there's no real difference between those, although the TIFF format supports layers, and PNG supports transparency – but this won't matter when simply scanning documents. All of them are supported very well by all operating systems these days.