Re: Do I need Origin when I brought the game on the EA app and/or Steam?
@Notfallkaramell Origin is no longer required in Windows. Anything you've bought through Origin should be accessible through the EA App, with the only exceptions being due to user-specific account issues and some download problems with the App.
If you still have the product codes from your CDs, and you haven't previously registered them in Origin or on the old Sims 3 site, you can do so now, and the content should appear in your EA App game library.
Steam requires neither Origin nor the EA App in order to run Sims 3 and never has. You also don't need to open Steam after you've run the game the first time—you can launch it by double-clicking TS3W.exe. If you're buying again anyway, I'd highly recommend Steam for several reasons, not the least of which is that you'd skip the current EA App download issues and any other problems the App will have in the future.
There's also the "Sims 3 Collection," a bundle that includes every expansion and stuff pack except for Katy Perry Sweet Treats (which is unavailable to purchase from EA as well) at a decent discount. It does not include the base game. The price is even better when Sims 3 is included in Steam sales.
If you do want to use Steam, you'll need to buy everything through Steam. Anything you own in the EA App won't transfer.