The Madrid chapter of your guide book will lay out multiple options for getting into town, but I used the Express bus 203, which takes you right to Atocha Station. You pick it up outside Terminal 1.
There's a left luggage office (possibly also lockers) at Atocha Station. Look for signs reading, "Consigna". If you use the office, you need to allow time for there to be a line when you return to retrieve your luggage.
I agree that you shouldn't try to do a big art museum on arrival day. I'd head to the area around the San Miguel Market. That's a great food source where you won't have to wait till 2 PM. The market opens at 10 AM (may differ on holidays), though it probably won't be very lively then. There are all sorts of tapas, including some that are egg-based.
If you need food rapidly, take the Metro from Atocha to Sol, then walk to the market. The Atocha Metro is not inside the rail station. It's on the other side of the traffic circle. It's good to have a map for orientation purposes; I always found that area sort of confusing. You may have to walk a good way before you see a street sign.
After exiting the Metro at Puerta del Sol, you can follow Rick's walking tour of that area or follow Calle Mayor WSW toward the market. Before you reach the market you'll pass very near the Plaza Mayor (off to the left). You should take the opportunity to see it.
After refueling, if you decide you need to spend time outdoors, you can return to the area near Atocha Station and enjoy Retiro Park for free and/or the botanical garden for a small admission charge.
You can walk between Atocha Station and the market in about 30 minutes. I'd do that both ways (taking two different routes) if I weren't starving upon arrival.
