Not driving, will have luggage.

Wondering how best to get from Seville to Granada, and from Granada to Madrid - considering where bus/train/plane stations are from key points of interest where we are likely to be.

Detailed instructions appreciated, especially where to be last in Seville or Granada so as to be logistically positioned to head for bus/train/or plane!!! Also, should tickets be purchased before leaving U.S. - where and how?

Many thanks!!

The Bus Station in Sevilla that serves the Sevilla-Granada route is Plaza de Armas. I don't know which Bus Company serves that route. It is advisable to get your reservation / ticket(s) a day or two in advance. If you speak Spanish you should be able to make your reservation by phone - such reservations are generally cancelled 2-hours prior to departure if you haven't purchased your ticket(s) by then.
P.S.
Buses normally have adequate storage space for luggage below the passenger compartment.

Alsina Graells is the bus company that you would want for Sevilla-Granada...its a short 3 hour bus ride (if not shorter), and there are several buses a day. Granada bus station schedule.....
http://canales.ideal.es/guia/autobuses_inter.htm
Costs around 30 euros round trip I believe. Be sure you reserve your ticket on the direct route, it you get on the ones with stops, a 3 hour trip could become a 6 hour long busride !
Kelly

I would recommend the train for the Sevilla-Granada leg of your trip ,take some olives,chorizo and a couple of beers in a cool bag,chill out and enjoy the scenery!.Make sure that you check that your carriage number corresponds to your ticket number.You can check this on the display screen inside the train carriage.The train station in Granada is a mite out of the city center but you can get a bus or taxi.For the Granada-Madrid leg it's gotta be the bus,but it's ok,it's comfortable and your luggage is packed away at the start of your journey. Granada bus station isn't great with the usual assortment of dead beats and thieves-the usual precautions for big citys apply!!
You're gonna have a great time!
Quien estuviera en Sevilla ahora!

You can get a "Bolsa Isotermica" at Cortes Ingles department store, and other places to keep your Mahous and bocadillos cold on the train and bus. It is an insulated silver mylar bag with a plastic fastener and handle which can be folded away when not in use. Everyone uses them, they are much lighter and more convenient than a plastic ice chest. If you have access to a freezer, take a little water out of a two-liter bottle of water (plastic), just a mouthful, and freeze it in the fridge, then use it to cool your sandwiches. As the ice melts you can drink it. If it doesn't melt fast enough, put it in a sunny place. I use this when I paint and it works great. A two-liter bottle of ice lasts all day.