Q: Moving from older iMac to newer model

I have a 2007 24" iMac running 10.5.8 at home and just purchased a new 27" 5K iMac. I used Time Machine to back up my old Mac via a USB 2.0 drive, but I am not sure about migrating anything over from the old to the new. I would like to have all of my files available if possible. I realize that most if not all of my software will need to be upgraded for the new computer. I use Adobe CS software as well as QuarkXPress. And some other odds and ends. What recommendations do you have for get me up and running as seamlessly as possible from my old system to this new one, with maximum utilization of the previous document, image & video files.

I would like to retire my old iMac, but understand that I may have to have it as a companion computer until I get smoothly running with the new system. Any advice is appreciated. Thank you.

~ Kort