I happen to use the date stamp, because I’m used to it, but you can also select View > Details (on Windows Vista and up, this may be more easily accessed from the icon button on the right of the toolbar) and click the “Date modified” column header to sort your backups chronologically.
It sounds like you’ve got backups more worked out now, so this may not be any issue any longer, but your description of how the file name was growing, appending additional date stamps, sounds a bit like you may be working in a backup file and then creating a new backup from that. I’ve seen a couple cases where users did this and got pretty nasty files names. Names aside, though, you want to avoid this since working in a backup means you no longer have a pristine backup to revert to if necessary and, in the case of automatic backups, it’s conceivable you could get yourself in a situation where you’re working in a backup that gets rolled off the list (should you end up opening another copy of the project with the same title and then get backups from that pushing off your other version). I hasten to say it’s rather complicated to get into a problem like that, but you can avoid it entirely by always being sure to copy your backup file from the Backups folder before opening it in Scrivener. If you’re backing up as zip files, you can open the zip in place and then drag the contained project .scriv folder to a new location (e.g. in your Documents folder), since that act of extracting the project is essentially making a copy; you can’t edit the zipped version.
Also, to answer your question about the “main project”, in case Ioa’s answer didn’t cover it, when you first create a project, you choose a location to save it. By default this is in your user Documents folder, but you can choose somewhere else. Whenever you open and work in the project, then, you’re editing that copy of the project; all changes are saved there, etc. Backups that you make, whether manual or automatic, are copies saved in other locations but aren’t touched again by Scrivener unless you go and access that backup to open it specifically. This is different from using Save As, which, as in other programs, saves a new copy of the project and also makes that new copy the new working version. So there, you’re working in project A and choose File > Save As and create a new copy Project B, you are now working in Project B and all further changes are saved to Project B. In the case of backups, if you’re in project A and back it up as Project Backup, you’re still working in the original Project A.
I hope that helps a bit! (I’m about to fall asleep on the keyboard, so if that actually just muddled everything further, I sincerely apologise…)