I make a habit of defaulting all my program outputs to a separate folder for the documents and such that they produce, so that I can just copy that folder for backups. That doesn't of course back up the programs that produce the documents, but for a new "clean machine" you're usually better off doing a fresh install of the programs anyway.
A few programs insist vigorously that the program "products" must be in the same folder(s) where the program is installed. You may or may not have any in this category, but ones to check out are usually the "small ones" like some music notation programs, "easy-x" programs from smaller producers like "Quicken," "My Software" (My Invoices, My Collections etc.), and sometimes your Income Tax program(s). (A couple of "genealogy programs" are notorious for this too.)
Before abandoning an old computer completely, it's a good idea to spend some "thinking time" about what stuff may be on it that is not deliberately and purposely put where it will get backed up.
If you can set up the new machine so that everything goes into ONE FOLDER (essentially equivalent to a separate partition on a hard drive) - with appropriate subfolders of course, you'll be set up for easier backups with the new computer.
Your email program messages and address book are two things that theoretically can be moved anywhere you want them, but in practice it seldom works as well as using the default locations. I wouldn't recommend, for most people, using a non-default location for them (for Outlook or Outlook Express).
Most other programs that "embed" the results usually are fairly small (or at least smaller than Windows/Office programs) so that it may be feasible to install the programs directly in the "backupable" folder and just backup the program(s) along with the data.
Looking at what you've got is probably the best way to figure out the most usable new setup. A little thinking-in-advance can be a big help, although it's not usually a "big enough deal" to agonize over.