How do I move Elements 11 photos and catalogue from iMac to new iMac both running Yosemite?

Question

I've been researching best way to move my photos and catalogue from my current iMac to my new iMac.  I'm using Elements 11.  Both iMacs running Yosemite.  I know I need to deactivate the current computer's version of Elements if putting it on the new one runs me over the license limit - I don't think it will.  I have read enough to be pretty sure I have to NOT migrate the Elements 11 program to the new iMac because it won't work properly - I'll have to reinstall it from my installation disc on the new iMac.  So far, so good. 
Now, I want the easiest way to get the photos on the new iMac, in the same folders, and preserve the catalogue and my current ratings on the photos.  I am unclear on how the catalogue works with its backup and restore function.  Should I move all my photos in their folders in exactly the same locations on my new iMac before installing Elements and trying to restore the catalogue?  I read about the ways to restore the catalogue and I am unsure about whether it just looks for the pictures in the places it expects to find them (which will be the same if I copy everything on to the new iMac first), or whether it restores the pictures where it thinks they should be (in which case I should NOT put the pictures on the new iMac before restoring the catalogue or I'll end up duplicating everything).   Also I have read - and been confused by - the options about restoring catalogue in new location, old location, etc.  I don't want my folders changed.  I have my pictures stored where I want them and I want to keep them there - and I'd prefer not to add some extra layer under the basic My Pictures on my iMac.
I have stored the most recent version of the catalogue, with all photos reconnected, on an external drive.  All the pictures in the catalogue have their meta-data associated with them.  I hope that this will allow me to preserve ratings.  Going through thousands of pictures to find the really good ones again is a time-consuming mess.  When I went from Windows to Mac 3 years ago - I lost the catalogue and all ratings.  When I upgraded from Elements 9 to Elements 11, I lost the catalogue and all ratings.  I do NOT want to ever go through that again.

Answer 1

I appreciate your answer and agree that it is correct, but you told me nothing I did not know.  There is an Elements technical paper which says this in much greater detail, but still does not answer the questions I was trying to ask.
The catalogue file seems much too small to include my thousands of photos.  Are you telling me that it has magically reduced the size of all those photos - from 64 GB to 33 GB, and added the catalogue information - so that the photos will just appear out of nothing but that smaller catalogue file when I restore catalogue?  If so, will you explain the options of same location, new location, new location with existing file structure, etc? 
I understand installing the program.  I understand that I should backup the catalogue (I've done it).  I understand I will use restore to restore the catalogue.  I found all this on other sites.  I need someone, somewhere, to explain to me if I need to copy the photos themselves to their new location before I restore catalogue - or not.  And which option in restore to use.  I thought I explained this in my original question.  Any help on these questions about matters I do not understand will be appreciated.