All already said is right.
Just to add, that there is a "Lufthansa Airport Bus" which connects the airport with the city (main station). Very clean and comfortable. Costs about 15 DEM each way (add some 20 DEM for the cab to your hotel so this sums to 50 DEM). Stops are just outside the Terminal buildings (A, B, C). Runs every 20 mins and takes about 40 mins. One stop at "Nordfriedhof" (25 mins)where you have the driver ordered a cab to pick you up, so you don't need first ride in to the city and then back to the hotel again.

Cab ride is about 100 DEM to downtown hotels.

Train station is a loooong way to go. Costs about 20 DEM and b/c it's not an express train but regular commuting takes as long as the bus ride will. Very frequent stops.

Any chance you stop by in DUS (and bring the evergreen clematis with you ?)