@Gaarel Any packs you own in Origin should be available to reinstall, for free. It doesn't matter whether you bought them in a store or directly from Origin. You can double-check that they show as owned in your Origin library first if you want. When installing the base game, you'll be asked whether you want to install your packs, and if not, you can choose to install them later. Origin will also probably try to download them the first or second time you launch the game, even if you disable auto game updates.
As for saves and Tray files, whether you need to set them aside depends on whether you want your previous content to be available after you reinstall. If you'd like to start fresh, just delete the Sims 4 folder in Documents\Electronic Arts. If you want to preserve your old saves, move the Sims 4 folder elsewhere, let the game create a new one after you've reinstalled, and then move the save files to the new folder. The same goes for the contents of Tray.