Thank you everyone for the advice. I just have a couple of more questions...

I arrive into FRA late morning on a Monday, so I will likely take a train around 1pm or so. I would much prefer to just buy the ticket once I get to FRA, but is that risky? It appears that there are a lot of trains going from FRA to Dusseldorf, so I am assuming that getting a seat should not be difficult. Is that assumption an accurate one?

Secondly, I looked on the DB site, but could not find any details about the different class of service. What are the differences between First Class and Second Class? My preference will be to buy a First Class ticket when I arrive into FRA.

Thanks for everyone's help!