Well, as far as partitioning goes, some will tell you that it is indeispensible, and others will tell you not to bother. I have run both ways, and the only real benefit I see for the average user, is that if the OS on one partition gets corrupted, then you can safely boot from the OS on the other partition.
Some video and audio pros use multiple partitions to save to for various reasons ranging from safety of the files to being able to defrag easily.
I say that if you are just going to use the machine for everyday things, just leave it all on one.
As far as migrating files, it depends on the old machine. If it is a Mac, does it have Firewire (the old one)? If so, just connect the computers through a Firewire Target Disk and transfer them that way. If no Firewire, you can connect with a crossover cable through the Ethernet ports, or if you have a CD-R on the old machine, you can just burn a bunch of CDs and then put them on the new one.
Hope this helps!
Regards,
Gus
EDIT: Here's a link on how to use Firewire Target Disk Mode
http://docs.info.apple.com/article....howSurvey=false&sessionID=anonymous|164608574