Partial migration?

For the past two years I have been using an older hand-me-down iMac in my office, and I am finally getting a new iMac this coming month. I'd like to migrate some things on to my new computer, but there are some issues....

THE PROBLEM:

The previous user did some serious voodoo to this current iMac. When I first inherited it, ALL the files were in the system root. And I mean every sundry mundane email message, word document and photo was dumped in there without any folder hierarchy or organization method. I have tried to clean it up as best as I can, but the computer has some serious issues, and the preferences on various software are completely messed up. I'll not list all the problems with it, suffice to say, I don't want to clone it, or do a time-machine type migration on to my new computer.

MY QUESTION:

Is there any way to do only a partial migration to my new iMac when it arrives? I obviously don't want any of the current system folders or even most of the applications, I will install all of those from scratch and hopefully they will run much better. What I really need to migrate are the gigs of archived files, my network settings, and my emails (the one application I want to keep).

Any way to do this? I'm not really sure where to start except maybe get a huge external hard drive and copy some things on to it....