How do I tell Firefox to only keep persistent cookies from sites I want?

You can pick and choose which sites you want to keep cookies from or want to block from ever getting.

Tools > Options > Privacy

The Options dialog will appear. This is where you set your cookies preferences.

To allow cookies to be set in the first place, check the following box:

☑ Accept cookies from sites

To keep all cookies from sticking, essentially turning them into session cookies (ones that won't be there next time you restart Firefox), select the option that will destroy them when you exit the browser:

Keep until: I close Firefox

To allow persistent cookies, ones that will be there next time Firefox is started, click Exceptions...

Type in the domain of the site(s) you want to always accept and keep cookies from. Click Allow for each.

If instead you would like to prevent certain sites from ever storing cookies, click Block.

When you've finished entering all the sites, click Close, then OK and you're done.

The CookieSafe allows you do this easily from the status bar. Set it to 'Deny Cookies Globally', then allow the sites you want.