Need help planning a trip from Copenhagen to Frankfurt

Take a train that goes onto the ferry Rødby - Puttgarden (using www.bahn.com to plan the journey). Lübeck and Hamburg are obvious choices that are on the direct route. Further south, Göttingen, Kassel and Marburg come to mind. Göttingen is not spectacular, but a nice town on the direct route. Kassel is mostly interesting for the Wilhelmshöhe park. Marburg is on the slower route towards Frankfurt, but worth the small detour.

Do check whether the pass is the best option for the trip (most likely, it is not).

I think a Eurail Pass would be a complete waste of money, but maybe its just my prejudice. Millions of Eurpeans ride the rails every year without any special passes. They buy tickets and go. Secret is they know how to buy them and save money. Its not rocket science.
Why do you need 1st class? 2nd class is great.
Itinerary? Luebeck, Hamburg, Cologne, Rhine Gorge day cruise, and you're a short cheap train ride from Frankfurt airport.

Kassel's Wilhelmhöhe is at its best when the waterworks are turned on (look at their website for timings).
Between Marburg and Frankfurt you'll find a string of smaller interesting towns: Fulda, Wetzlar, Limburg and Weilburg.
Do the arithmetics to see whether a pass is a good deal. Probably not. And you know the opinions on 1st class: 2nd class is comfortable enough, also on regional trains.

I think first class can be worth it. The difference is not huge, but it is usually more quiet and a tad more comfortable. The saver fares in first class are sometimes just a few Euros more expensive than second class.