Outgrown computer

I currently have all my files on one computer, and backed up onto 2 separate hard drives (R1 and R2). I'm outgrowing the computer and need to know the steps I should take to move my primary copy (the one now on computer) to a separate drive, which I can then backup, presumably on those same 2 externals drives. Can I plug the new 'main copy" into my "new" computer (the one with no photo files on it, at this point, except for "working files") along with a backup (call it R1) and then sync files from one external drive to that R1 backup? It's been a while since I set all this up...so trying to remember and do it methodically, so I don't lose anything!

Mary