@Mermaid_Ellix It doesn't matter when the rest of the discs were manufactured, just the base game. If its copyright date (on the back, in small print) says 2013, then you'll have to play through Origin no matter how you install.
The later base game discs require you to install Origin before installing TS3, and on these kinds of installs, you can't launch the game unless you're logged into Origin already. This isn't true for older discs—you can install and launch the game without having Origin on your computer at all. You just double-click on the shortcut on your desktop, and the launcher loads without any Origin involvement. Some people don't mind having to sign into Origin before playing, but others don't like it running in the background, or they have spotty internet and worry about not being able to play if their connection goes out.
The other issue is that patch 1.69 added a pack selector to the launcher, so players have to check boxes to indicate which packs they want to load before pressing play. This pack selector has been known to forget which packs you previously checked off, and it sometimes deselects packs while leaving their boxes checked. So you don't know that there's anything wrong until you load your save, and items have disappeared (or the save can't load at all). Then you have to quit to desktop, uncheck and recheck all the boxes, and hope that your selections stick this time.
But again, all of this is a moot point if your base game is one of the newer ones.
P.S. I didn't see your additional comment until now. If you're comfortable with the way an Origin install works, then there's no reason to change. But please don't sell your discs, especially if your copy of the base game is one of the newer ones. The buyer won't be able to register the codes in or install through Origin, so if an all-disc install isn't possible, the discs will be worthless. Sorry, I confused the two posters there. The point stands about not selling discs, but I clearly didn't pay enough attention.