How do I save my progress in the game to a new computor?

@LirraFlirra  It's best to launch the game once on the new computer, both to make sure it works and to let a new Sims 4 folder be spawned in Documents\Electonic Arts.  Then you can copy your existing files into the new subfolders, e.g. your save files go in ...\The Sims 4\saves, your saved households in Tray, etc.

If you're transferring mods or custom content, especially if you're switching from Windows to macOS or vice versa, you may need to zip the entire Mods folder before moving it to an external device.  Right-click on the folder to see the option.

Here's a list of everything in your Sims 4 folder you might want to transfer:

https://sims4.crinrict.com/eng/2014/09/user-files-explained/