Just a few additions to all of the above good advice.
Atocha Station is indeed very confusing. I'm used to navigating Penn Station in New York, which is insanely confusing, and I still had difficulty in Atocha (and I wasn't even jetlagged). So do allow plenty of time, ask a lot of questions, and take it slow.
There are no checked bags on these routes. You have to schlep all your bags yourself. This is true for both the trip from the airport to Atocha, and then from Atocha to Seville. Pack accordingly. On the AVE from Atocha to Seville, there is storage space above your seat as well as a rack for larger bags (the Seat 61 website should have pictures of this).
However you get to Atocha, you will have to go through a security check before you can board your train to Seville. It doesn't take long, but it does mean that you can't run to the train just one minute before departure.
AVE trains from Atocha leave from two different levels; check the departure monitor carefully to be sure you go to the right level, and if you're not on the correct level, ask how to get there (again, I had trouble with this).
When you buy your ticket from Atocha to Seville, it is for a specific train departure and so comes with the necessary reservation; you don't get the reservation separately (unless you were using a railpass of some sort). That's the catch - you won't be ready to get your Seville-bound train until you've gotten to Atocha and finished buying the SIM card, and you don't know exactly how long all of that will take.
Getting the SIM card throws a monkey wrench in the works. If you weren't getting a SIM card, you could buy a ticket at the airport for your Atocha to Seville train, and the Cercanias train from the airport to Atocha would be included (there's a code on the ticket that works at the Cercanias machine - ask the ticket seller to show you how). The ticket seller would be able to estimate how long it would take you to get to Atocha from the airport and so could sell you a ticket for the correct train, and you'd be set. But you don't know long the SIM card purchasing process will take, so it may be difficult to pick your train departure time while still at the airport.
If you don't want to take the Cercanias train from the airport to Atocha, a taxi has a fixed rate of €30 and no tipping is required beyond this.