Can you recommend a good, reliable backup software?

So, I have an old Seagate external hard drive that I’m using with my laptop. Both laptop and Seagate drive are now very “long in the tooth” and it’s time to get new equipment.
I’ve been very happy with the way the Seagate drive works. It came loaded with backup software, which seamlessly, effortlessly, and unobstrusively backs up my files.
Here’s what it does that I like:
1. It backs up only those folders that I designate.
2. It backs up only files in those folders that are new or have been modified (i.e., incremental backup only).
3. It saves any older versions of those files into a “history” folder.
4. It keeps as many generations of history as necessary.
5. Any deleted file is also deleted from the current generation backup.
6. All backups are encrypted.
7. It does all of this silently in the background.

Now, I just bought a newer external hard drive with much larger capacity to go with my new laptop (not yet purchased), but it does not have backup software.
Can you recommend a good backup software that works as described above?

Thanks!