The Madrid-Granada line is not the high-speed AVE line yet, but still the train is clean, quiet and convenient. Trains run on time except for unforeseen issues/accidents or scheduled track work.
Spanish trains offer a significant discount for advanced purchase. Try and book 60-90 days in advance to assure getting a discount, but often they are available even closer to your dates (there are only so many discounted tickets available for each train).
The Spanish rail site renfe is notorious to navigate and understand, and even harder to use a US credit card. But take some time to figure it out, consult the tripadvisor Spain forum thread on renfe and use the Paypal option for payment.