OK, both Macs have a Firewire 800 port. That's good. The first question I need to ask is which OS do you eventually want on your 2007 iMac? Yes, you have Mavericks, but your machine can run Yosemite (OS 10.10.3).
Secondly, please describe exactly what you mean by "starting over". If you mean you want to start from the very beginning, the process will involve, at the start:
1. Erasing, formatting, and partitioning the drive inside the 2007 iMac.
2. Installing either Mavericks, OS 10.9 or Yosemite, OS 10.10, onto that machine. (You can first install Mavericks, see how it runs, than upgrade to Yosemite. However, you need to realize that for any third party applications that you have, you might need to upgrade those also, so that they can run "under" Yosemite).
3. Applying the OS 10.9.5 Combo Updater to get to OS 10.9.5, the last version of Mavericks, or the two OS 10.10.3 Updaters (one is the Combo, the other is the Supplemental) to get to OS 10.10.3. (There is also a recent version of Safari for Yosemite that came out after the Supplemental Update).
From there, you would need to get any of the applications you want installed. Also, do you have any files/folders currently on your 2007 iMac which you need?
The only other possible "concern" is the health of the hard drive currently inside the 2007 iMac. If it is the original, it is 7 years old, and hard drives "tend" to start having issues at the 5 year point. But, that is not a "hard and fast" time frame. There are a few things which can influence that time line (how often was the drive used, whether any disk maintenance/repairs (from a software perspective) have ever been done), etc.