If you buy a Saver Daypass, you can ride essentially ALL of Switzerland on that day; most of the “nice” mountain railways are NOT included, but Rigi IS included.
If you get to the booking page(s) for Saver Day Pass, they quote 1st and 2nd class with and without a ½ fare card–either way you get FULL GA coverage.
The actual purchase may not work with many credit cards. From the USA AMEX do work.
If you are only taking this one trip, there is no monetary advantage of buying a ½ fare card; Rigi is one class, so 1st class is probably not needed.
A nice routing to get to Rigi: take the boat from Luzern to Vitznau and the Cog Railway up to Rigi Kulm, most train trips meet the arrival of the boat.