We traveled from Toledo to Sevilla last spring. My son is disabled, so we are slow to make connections as well. I allowed us one hour at Atocha between arriving from Toledo and catching our departure to Sevilla. It was plenty of time. I think 30 minutes would have been a little tight for our first time, but I would feel comfortable booking that now that I have been through the station and know where to go.
Edited to add: look for the elevator (acensor) in the track area that will take you up to the trains departing for Sevilla. Ask a Renfe employee if you can't find it. Taking the elevator will speed up your journey through Atocha.
When booking tickets via Renfe:
If you click on the "Welcome" button at the top of the Renfe home page, it will load in (mostly) English. Subsequent pages may be mixed English and Spanish. After you input your departure (Madrid -- Todas), destination (Sevilla -- Santa Justa), date, and number of passengers, you will then get a list of available trains. The AVE trains are high speed. If you click on the "Opciones" (options) plus sign, you will see a list of available classes (clases) and fares (tarifas). Preferente is first class, Turista is second class. Promo fares are nonrefundable and do not allow changes; flexible fares do.
Promo fare does not allow you to select your seat, but if you are traveling with multiple people, your seats will be automatically grouped together (assuming seats together are available). I think (but I could be misremembering), that you may get to see the assigned seats before you purchase, so that if you don't like them, you can cancel and start over.
I found Renfe easy to use, but I speak Spanish :-) If you have trouble with payment, use PayPal, which worked flawlessly for me.
This TripAdvisor link was helpful to me for using Renfe (thank you to Harold, who posted this a long time ago):
Buying Renfe Tickets Online
I second the recommendation to take the bus between Sevilla and Granada. The current construction on the train line into Granada means you have to transfer from the train to a bus at Antequera, so it is simpler if you have mobility challenges to just stay on one bus from start to finish. The ALSA bus was comfortable, cheap, and easy, and it didn't take any longer than the train.
Have a great time on your trip!