New computer

@geodigm  Your saves and other user files (mods and custom content, saved households, etc.) are stored locally on your computer.  Sims 4 doesn't support cloud saving.  So in order to preserve that data, you'll need to transfer the content manually.

The user data is all inside Documents > Electronic Arts > The Sims 4, and you can transfer this entire folder or the subfolders you want to keep, e.g. saves and Tray (saved households and builds).  I would suggest zipping the folder(s) before the transfer and not unzipping until the data is on your new computer.  This helps protect files from being corrupted during the process.

Launch the game on the new computer once to make sure it works, then move over the files you'd like to keep using, and you can pick up from where you left off.  Where the game has created a new file or folder, it's best to use that instead of the old one, for example move over the saves themselves, not the folder they're inside.