The problem with JPEG is that its compression algorith is lossy, meaning it drops some data each time it is used. In plain English, your file gets worse every time you save it. Thus, you want to make saving in JPEG format the last thing you do before uploading.
But often times you will want an original copy that you can later work on without having to rescan, or perhaps you are scanning in one program and editing in another, or making edits in more than one program. Thus you will need to save your image in a format that does not lose data each time like JPEG does. TIFF is one such format that is popular; personally I use PICT which is a more common format on the Macintosh. But both TIFF and PICT are much too big to be used on the Internet. For example, one of my photos that I have in both PICT and JPEG format on my hard drive is 1.4MB as a PICT, and 92kB as a JPEG.
Regarding your second question, I don't know Adobe Photo Deluxe specifically, but in most of the image editors I have used, there is some sort of "Options" button in the "Save As" dialog box, if you click it while JPEG is selected as your format, there should be some sort of option. It could refer to either "Compression" or "Quality". For Airliners.net, you want maximum Quality or minimum Compression. This is because Airliners.net has its own routines to optimally compress the image, so you want to give them the best image you can to start with. These files are generally pretty big, so if you are uploading them to your own site, you will want to save another copy (from your TIFF original, not the JPEG you just saved; see what I just wrote above) with a slightly lower Quality setting or slightly higher Compression setting. In one program that I have used a lot, GraphicConverter, the setting refers to Quality. Airliners.net images saved at 100% Quality are often over 400kB, while versions of the same imaged saved for my own web site are done around 75% Quality and file sizes tend to hover near 100kB, with very few visible differences.