Manually restore files/folders from full backup to new install

Hello everyone. I'm in quite a pickle here. My 3 month old Seagate SSHD failed that I had installed in my Early 2009 iMac. Luckily, I had a backup. Unluckily (if that's a word), the backup (which was made using CCC), will not boot for some reason. The loading bar (new to Yosemite) freezes halfway, and will not boot at all. It won't boot in safe mode either. I checked verbose mode and it gets stuck at an en1 error or something. Also, when I try to clone the external backup drive to the replacement internal drive, it freezes at a file in the /usr folder. Anyway, I have already decided what I want to do.

Here's the plan:
I would like to put a fresh install of Yosemite on the replacement internal drive, and copy all of my files and folders manually from the external drive. How would I go about doing this? I would want to keep every User (there are 5 of them), as well as Applications, app settings, system settings, wallpapers, startup items, etc. Basically as much as possible. Everything that I can transfer over after a clean install I would like to transfer.

Does Migration Assistant in the Startup Assistant do all of this for me? Would it be like using the same computer afterwards?

Any help is appreciated.