I understand that there are many trains from Madrid to Murcia, and the station is not Atocha. What is the name of the station? And how long does it take to get there from the airport between 8 and 10 AM? Taxi? Thanks!

These trains start at Madrid Chamartin in the north of the city, but head south and also stop at Madrid Atocha Cercanias (the suburban 'through' platforms as opposed to the terminus platforms, but all part of the same Atocha station).

So take your pick, Chamartin or Atocha. Atocha is nearest the city centre.

Check train times and buy tickets at www.renfe.es

Thanks.............so are you telling me that I can catch the train from Atocha to Murcia and I don't have to go to another station? A little confused. Thanks.

'so are you telling me that I can catch the train from Atocha to Murcia and I don't have to go to another station?'

Yes. See the link already provided.

Yes, but they stop at a different "section" of Atocha ( CERCANIAS) for a QUICK stop.

Thanks to both of you....can I get tickets for this train at the airport so I have them in hand at CERCANIAS?

Yes - http://www.renfebarajas.com/english/contactar.htm#

If I do not get my train ticket ahead of time on the Internet, is there a chance I will not get a seat on the train from Madrid to Murcia on a Friday (1/28) leaving Madrid at 12:30 PM? Also, looked at the RENFE site and what's the difference between 'turista' and 'preferente' and there is one other classification (besides price)? Thanks.

a chance.. yes. how much? who knows.

turista is tourist

preferente is first class, gets free food, unlimited drink (just keep asking) and use of VIP lounge and snacks ahead of departure at station.

Cerecanias simply means 'suburban' as opposed to 'main line', a general word not the word for the station! Go to Atocha, and follow the signs to Atocha Cercanias.

Cheap tickets can be bought in advance, more expensive tickets on the day, a bit like airlines. www.renfe.com to pre-book.