Eurail Spain or Renfe Spain pass?

Unless you are all students, there is often little value for a pass. Your best savings is to book as early as possible. Renfe posts routes 62 days out but also sometimes in month blocks so it could be as much as 90 days ahead. Savi gs on some routes and tkmes to 65%. Also, with 4, you can book a Mesa fare which is a table for 4. Price is entire table. It is still a savings, even if not early, earky booking.
One challenge is US credit cards can be finicky. You can use PayPal, however.

FYI, differences between the passes:

• The Eurail pass counts full calendar days of travel, from midnight to midnight. Seat reservations cost extra, can be booked in any order, and may be limited.

• The Renfe pass counts each different train that you board. All of your mentioned routes can be done by direct trains, so that might not make a difference for you, unless you add a stop in Cordoba, etc.. Seat reservations are included but must be done on Renfe's web site in the same chronological order that you plan to travel.

Regular train tickets are all sold for reserved dates, times, and seat assignments, whether at full fare or one of the advance-discount rates.

The seat61 site should answer most of your questions.

The best way to book these trains is direct from the Renfe site: https://venta.renfe.com/vol/home.do?c=_fTCW

You will need this tutorial from TripAdvisor: https://www.tripadvisor.com/Travel-g187514-c80518/Madrid:Spain:Buying.Renfe.Tickets.Online.html

Use Paypal, as US credit cards rarely work on the Renfe website, while Paypal goes right through.

If you hurry and are flexible with your departure times, you should still be able to get some good fares.