JPG format has a magic status for us. JPG is wonderful when the purpose is right, but we need to understand we pay a cost in quality. I know you surely will consider using JPG for master copies, everyone does at first, because the JPG file is so small, and the idea is frightfully appealing. But it's a high price paid in lost quality, and you will eventually come around to appreciate the quality of TIF files. I hope that happens before you have damaged important images that you cannot scan again. Some people argue that high quality JPG masters are not so bad. That's OK with me, it's your file, but the file size is one property of an image, and quality is another. You can choose either way, and I hope you choose Highest Quality, at least for your master copies. My goal is that you understand the effects of your choice in regard to your valuable master copies.
If you simply must use JPG for your master copy (if file size is the most important property of this image), then at least use the best Quality you can. Aim for a average JPG file size at least as large as 25% of its true memory size. For web images, file size is indeed important, and absolute quality is less important, and a JPG file size 10% of uncompressed size is often a good tradeoff of quality for size for color images, but that is too extreme for any notion of a master copy. Grayscale images do not compress as much as color at the same settings. Grayscale is already 1/3 the size of color, and grayscale JPG files won't compress as much.
Then keep a master copy that you never rewrite. For any purpose, always start with a copy of that JPG master and never modify that JPG master itself. Saving that JPG master image again causes more artifacts, even more loss, permanent loss, so simply don't do it. If you simply need to rotate to vertical, or to scale for printing, consider not saving that simple change at all if it is trivial to do again. Save any change to a different file, and never make your one master copy worse. Or save the change to a TIF file, so as to not create more JPG artifacts. You could just use a TIF master instead, and sleep better at night. And be aware that lowering scan resolution to reasonable values for the purpose is often the best size reduction you can make.
Judge your own common sense periodically. Why can't we see that a decent JPG image compressed to be only 25% of original size (1/4 size, still amazingly small, and still with mild artifacts), is more useful, and a much better deal, than one at 5% size that is simply too awful to use? I know, the macho types are saying "but I can get it down to 3%". Then go for it man! 😊
For emailing and for web pages, JPG file format is the smallest by far, and the best goal by far (for photo images). JPG is acceptable for such read-only "viewing" use, and a JPG copy normally is used for such purposes. JPG is NOT very acceptable for "editing" use, when you may need to edit and save the image again (we always do). JPG is best only for photographic images. For line art and graphic files (characterized by containing graphic sharp edges and very few but solid colors), then TIF LZW or PNG is good, or GIF files too, which have historically been used for graphics on web pages.
The process of saving a JPG file to disk first compresses the image data to make the file be much smaller. This JPG compression affects the image quality, because JPG compression uses a very different technique than does PKZIP or TIF LZW or PNG file compression (lossy vs. lossless). JPG compression is extremely effective, because it does not attempt to be 100% faithful to the original image data. If parts of the image data are a problem for it, the JPG compression simply modifies that data to make it conform better. That means when we read that JPG file later, we don't get back the same original image data (that is the meaning of lossy, losses of image quality). Also the software opening that JPG image does a similar thing when it reads it. It does not necessarily show exactly what is in the file, it can also take similar liberties. Web browsers for example are not the best JPG image viewers, but they are the fastest JPG viewers.
Every time we save a JPG file (menu FILE - SAVE AS - JPG), it compresses again, and image quality is lost. This loss is variable, depending on the JPG Quality factor used, but it is never zero. If we edit the JPG file image and save it again, then quality is lost again. Even if we save it at a much higher quality setting the second time, it is still a second compression and another loss. Every time we compress a JPG file, we add more JPG artifacts and lose a little more quality. Artifacts are always a one way trip, there is no recovery. The damage is done.
Most other file formats (say TIF or PNG) use lossless compression. These files are larger than JPG because they use milder, fully recoverable (lossless) compression to carefully preserve all of the original image data. These file formats remain full quality at all times, no matter how many times we might save them to a file, which is exactly what is needed for a master copy.
The small JPG file size is great, but it has a big price of reduced quality. There are proper times and places one would use it, and also major reasons one would not. There's nothing wrong with creating a JPG image using a moderate to high Quality factor to put a photo image on a web page or to send it via email. It's the only practical way. However there is an additional quality loss when we try to edit and save that JPG file a second time, so JPG is usually inappropriate for important archived master copies. The risk if you make this mistake now is that you cannot undo it in the future, so now is the best time to understand the situation.
See the very worthwhile JPG FAQ by Tom Lane
Progressive JPG is a web option that quickly shows the entire image in very low quality, and the quality fills in and improves as the file download completes.
A new JPEG 2000 file format is available now in many newer program versions, with various file extensions, normally .jp2 (or .jpx, with option extensions). JPEG 2000 uses a wavelet compression method. It has a lossless option (to perhaps 65% size). Otherwise it is lossy, size comparable to regular JPG files, but different... slower then JPG, but arguably perhaps better quality. Extremes of compression have few detectable artifacts, however JPEG 2000 images become noticeably soft with greater compression.
Paint Shop Pro 8 and PhotoImpact 8 started including JPEG 2000. Adobe Elements 3.0 includes JPEG 2000. Elements 2.0 has an update to add JPEG 2000 at the How To palette, Select a Recipe, Download New Adobe Recipes, then (very important) the BACK button, and you will see it. Photoshop has an optional JPEG 2000 plugin from CD, see JPEG 2000 at the CS or CS2 Help menu.
Note that web browsers do NOT support JPEG 2000 yet, and so compatibility is still a very significant issue. Therefore it seems important to stay with the original JPG format for now, at least if you want others to be able to open your files.