Quick question about backing up saved games

[jsharp96]

I am in the process of upgrading the hard drive in my fat 80GB PS3. I am upgrading to a 500 GB hard drive. I did the system backup last night and backed up to an external hard drive. I will be switching the hard drive out and replacing it in the same PS3. Since I am backing up and restoring to the same system, will all my files be transferred? My research has told me I'm fine as long as I'm restoring to the same system. I just want to make sure I'm not going to lose a bunch of saved games because of copy protected files. Will I be fine simply restoring to my old PS3 with a new hard drive, or do I need to join Playstation Plus for three months so I can utilize the cloud storage? I realize there are tons of threads on the topic, but I've noticed a lot of them are dated. I know there have been some changes with new firmware and cloud storage, just want to stay on top of things. Thanks in advance!!