Frankfurt airport has two train stations. One is the regional/local train station the other one is the long distance train station. Both stations are clearly marked and easy to find. Just follow the signs. Since you want to get to Düsseldorf you will go to the long distance train station.
To buy a ticket from Frankfurt Airport long distance train station to Düsseldorf mainstation just visit
Deutsche Bahn (english). You can print out your ticket at home, send it by postal service or just buy it at the train station at one of the ticket machines which accept credit cards.
It is hard to say how much time it takes after arrival to get to the train. If you are arrive at Terminal 1 (mainly Lufthansa and Star Alliance) get through immigration fast and get you luggage quickly 60 minutes can be enough. On the other hand it can take much longer.
Luggage is no problem as long you can carry it by yourself. The ICE trains are not known for their huge baggage compartments but one suitcase is no problem.