Refer to this:
Yes, at this point you can only use the standalone DNG converter to treat your files, but any current Adobe product will be able to handle them natively by ways of ACR. As for the programs - that entirely depends on what you do. Most professional photographers and ambitious hobbyists use LR and PS (the big one), PSE will probably disappoint you because compared even to PS CS2 it is limited for "serious" imaging work.
Note that Camera Raw exposes fewer features when used as part of Photoshop Elements.
LR 4.3 RC and ACR 7.3 RC will support the raw format of your new D600 camera. Both are in public-beta phase, now, which precludes using Elements until ACR 7.3 goes into production in a few weeks.
To get started doing something right away, get Lightroom 4.3 RC from Adobe Labs and try that on your new computer, and use Edit In Photoshop (with LR Adjustments) to do things beyond what LR will do. LR 4.3 RC will expire in a couple months, but that should give you enough time to get comfortable with it or decide you don’t want to use it. http://labs.adobe.com/
Once ACR 7.3 is released to production, you can download and try the PSE11 trial and update it to ACR 7.3. As Noel says, the raw-processing user-interface exposed in Elements doesn’t give access to the more sophisticated adjustments that LR and ACR with PS-CS6 would and PSE also doesn’t have nearly all the functionality of PS, either.
Of course if resources are not too much an issue, the PS-CS6 starts at $600 or a monthly fee of $50 for a Creative Cloud subscription and you could also use it with the ACR 7.3 RC beta from Adobe Labs. Your CS2 is too old to quality for upgrade pricing.
As someone who has both LR and PS, I use LR most of the time and occasionally use PS for finishing touches.
Also, if you were merely looking for the Adobe Application Manager 6.2, you can get this by searching http://www.adobe.com for Adobe Application Manager 6.2.
Here is a link to the Windows version: