Frankfurt airport to Nuremberg

No problem buying tickets at the station. German trains don't have compulsory seat reservations so even if there are no seats you can still stand on the train.

No separate luggage compartments on modern trains, so you need to carry and store your own luggage. Some ICEs only have racks above the seats, so you will need to be physically able to lift your cases above your head. Others have racks at the ends of the carriages for large luggage as well. The risk of luggage theft on trains is much overstated, but you may want to bring a chain to lock your cases to the racks, if they're at the end of the carriage, and avoid leaving very valuable property or key documents in cases that aren't over your head. Especially since I believe Frankfurt Airport to Nuremberg trains make several stops along the way, which is the point of biggest risk for the whole case to be stolen.

Here is a map of the airport Fernbahnhof (long distance train station).
http://www.bahnhof.de/file/bahnhof-de/6493602/beJf7TCNmc3deZGD7rL2-zkz87Y/6506964/data/Frankfurt%20am%20Main%20Flughafen%20Fernbahnhof_de_PDF.pdf
Top floor orange block is the DB Reisezentrum (ticket office). There are elevators down to the track level.
When you collect your luggage, you can get a free luggage cart. After exiting customs, follow the signs and little train icons to the train station and buy tickets. There is at least one ICE train to Nuremberg every hour. Your 1st class tickets will have seat reservations and car number and which track the train is going from. There will be a graphic display on the platform that shows a map of the train so you can go to the spot on the platform where your car will stop.
You will be responsible for loading the luggage on the train. I am not sure if you can bring the luggage cart on the platform. If not, you will have to load the luggage on the elevator and then head down.
There are spots in the train car for luggage. I don't think you will have to worry about it. I never do.
View schedules and info at www.bahn.com. 1st class seats should have seat reservations included. Looks like the price is 97 euro per person bought at the station.

"have read the information provided on the Euro Railways website"

Third-party ticket reseller. Get all your information on train travel in Germany from the actual rail operator, Deutsche Bahn.

"Will we have problems getting tickets at the station?" Not at all.

"but we plan to get 1st class tickets on the ICE train" Well, it's your money, but is there any particular reason you want 1st class? The seats are exactly the same size. The only differences are that they provide more space for business travelers to do work en-route, and you get waiter service. Also, usually less crowded. But for most travelers' purposes, 2nd class is more than adequate.

"What is the luggage compartment situation on these trains". There is no luggage compartment. You store your luggage on the rack over your seat, and if there isn't enough room, there's a larger rack usually in the middle of each carriage.

"will the luggage be safe if out of our view?" Luggage theft on ICE trains in almost non-existant. Think about it. Tickets are costly and the trains stop infrequently. Stealing random bags from unsuspecting tourists with the hope that the contents contain objects with enough street value to offset the cost of the ticket and high chance of getting caught before leaving the train seems like a pretty terrible business plan to me.

A big THANK YOU to all of you for taking the time to reply. You've helped us tremendously!

One more thing. Since you say you are each bringing 2 large suitcases, I assume you are flying Business class over and get the extra luggage allowance. Just because you are allowed 2 checked bags, doesn't mean you have to bring them. Life will be a lot easier if you limit yourself to one large suitcase per person. The train stops in the airport station for exactly 2 minutes. Personally, I can't imagine bringing that much stuff on a trip to Europe.

Sam, thank you for your suggestion of packing more sparingly and no, we are not flying business class so we're not bringing 2 large suitcases just because we can. We have to accommodate necessary medical equipment. Wish we could pack as lightly as you obviously do but we don't have that luxury.

Sometimes you might be lucky enough to find room between the seats that will fit your bigger luggage. We have been able to do that sometimes. Sure wish I was making that trip in 2 weeks! Have a great time!

If I had my choice I would fly to Nuremberg but my husband is fearful of flying so he doesn't want to get on a smaller plane after the long haul flight.

In fifteen years I've only used ICEs nine times, but this is my experience.

On three of those trains, I had seat reservations and didn't need them.

On one of the other six I didn't get seat reservations when I bought my ticketts and it was SRO. After half an hour, we approached the next station, people got up to get off, and we took their seats. Although every seat was occupied, maybe only half were already reserved. Had we bought reservations when we bought the tickets, there would have been seats available. That was on a major holiday.

Three years later, not at a busy time, I rode the same train. I asked when I bought my tickets if I should get a seat reservation. The clerk very coyly said that I could if I wanted to. I declined, and I was one of three people in the entire car.

So, if you are really concerned, purchase seat reservations when you buy your tickets. You probably won't need them, but for only 4,50€/seat, it's cheap reassurance.