New computer needs backed up files

Hi there,
I replaced my failing W7 machine with a W8 one. My old files are backed up on a USB drive and I want to put many of them on the drive of the new machine. When I look in the backup folder on the USB drive I see the files but they are all zip files.
The old computer is toast. What is the best way to recover those files to the new computer. Ideally I'd want to do it in one go ...adding missing files from the backup to the new pc, but not as zips, and not adding any files with the same names that are older than the files on the new machine.
Then I'd like to put Sysback on the new machine to do ongoing backups to the same backup folder on the USB drive.
Hopefully I was clear on that and can get advice on it.
Thanks in advance!