Trains

I think a lot of the answers depend on personal preference.

Recognizing that you have undoubtedly found this page, here is Renfe's explanation of seating in different classes:
https://www.renfe.com/es/en/travel/el-viaje/on-board/tipos-asiento

Basico, Elige, and Premium tickets also have different rules for ticket changes or cancellations. Basic - no change allowed, Elige and Premium more flexibility.

Booking now for May could be a bit early, sometimes all the options don't show on the Renfe website.

If you want one reference point for consideration using my personal preferences/biases/comfort levels - I booked my similar train routes about 1.5 months in advance of my non-high season travel dates. I booked after monitoring the website for about 2.5 months out looking for price changes and watching as additional departure times were added. I built in some flexibility by purchasing above the Basico level. I suspect I could have done a walk-up, but it is my preference to have a plan with ticket in hand and adjust on the fly as necessary.

Personally, I would not opt for first class, the basic is fine.

I would buy the Madrid/Cordoba and Granada/Madrid tickets ahead, if your dates are locked in. The Cordoba/Seville segment, flip a coin, it is a short trip and there are likely lots of options including regional trains.

As for the Tarjeta Dorada, for the small cost and hassle to get it, and having to wait until you get there, for three relatively short trips, I wouldn't worry about it. You wi8ll save more by buying ahead.

Your timing is perfect. As above— forget about the Tajeta Dorada card which offers 40% off “Regular” train fares ( the most expensive). Instead, buy your high-speed train tickets NOW from the company Renfe contracts with to sell its tickets. www.TheTrainline.com is where you can score all your train tickets for Madrid Atocha to Cordoba ( for as little as $29) Cordoba to Seville Santa Justa ( for as little as $21) and Granada to Madrid Atocha ( for as little as $38). These are the deeply- discounted prices available on some days. The biggest discounts are for the “Basico” tickets in 2nd class. These are non-refundable tickets, so be certain of your departure dates and times before buying the tix. Have your Passports and credit card handy to process the ticket purchases. The Trainline will give you the senior discount without the Tarjeta Dorada card and train conductors just want to see your digital ticket on your phone— they don’t ask to see the Tarjeta Dorada card.
Have a great Trip!

I'm not sure whether Kenko is suggesting that you buy senior tickets and then travel without having a Tarjeta Dorada, but you should not do that. I don't remember what happened during my most recent trip to Spain (2019), but I've used senior tickets often in Europe, in a variety of countries, and I have quite often been asked for the qualifying document. If you're asked for your Tarjeta Dorada and don't have one, you can expect to have the book thrown at you in the form of a very high fine.

I’m not suggesting anyone do anything prohibited. In Spain, you are eligible for the senior category if you are 60 years old. The Trainline will collect your Passport information including your birthdate when processing a ticket purchase. A Tarjeta Dorada card number is not required to process the purchase. It could be that you are getting a nominal reduction ( it’s certainly not the 40% reduction off “regular fares” ). The Trainline has legal contracts with Renfe to sell Renfe’s tickets under provisions of their contract. I doubt The Trainline would risk renewal of their contract by doing something Renfe prohibits. If anything, a conductor might ask to see your passport to verify your identity matches the one on your ticket. Your DOB is also on your passport for verification.

The new high speed operator in town, Iryo, has my Seville-Madrid tickets priced 10 to 20 euros less than what I can buy Ave (high speed) tickets for through either RENFE or Trainline next month. Their exchange/refund rules are much nicer too.

Do yourself a favor and check out their very competitive pricing at their website www.iryo.eu. I think you’ll be surprised.

We travelled to Spain earlier this month, taking the train Seville to Granada; Granada via Madrid to Barcelona. We booked our train travel with Rail Europe. I did look at the Renfe website for timetables however found Rail Europe easier to navigate when booking. After researching, most information recommended forgetting senior discount card and recommended pre-booking. If you need to be in destinations on specific days, personally I am more comfortable booking in advance.

We did have an issue in Seville as our train was not on the departure board. Turned out the train was delayed. We went to the Renfe Customer Service office. They were very helpful reissuing our tickets for another train.
As for choosing level of ticket. We tried both 1st class and second class. For the 20 euro extra, and if it’s affordable for you, it is well worth opting for 1st, especially if it is a longer journey. Second class is fine but more chaotic and the seats narrower, less legroom and not as comfortable as 1st. There are no other perks with 1st, and we had to pay for coffee and snacks. The train between Seville and Granada had no food service. Therefore, I would recommend purchasing a sandwich, coffee/water before boarding. There are cafes at each of the stations in these locations. Trains were clean and the Renfe staff were lovely. Stations were easy to navigate. If you are not sure that you are in the correct area… just ask at the info desk or staff member. Very helpful and we found everyone could speak a little English. Allow time for security as your bags will be put through X-ray. However it is a simple and fast. Enjoy!