You don't need reservations.
You can buy tickets after arriving at Frankfurt Airport.
> once we arrive at the train station in Frankfurt
Frankfurt Airport has itself 2 train stations and also DB (German Rail) travel centers where you can buy tickets.
> Will having our luggage with us pose a problem with respect to seating and storage?
As long as you can handle your luggage: no
Best option are Rail&Fly tickets you (may) get from your airline.
bahn.de/international/…rail_fly.shtml
Cheapest option is to use regional trains on a Hessen-Ticket. EUR 30,00 for both of you. This day ticket covers also trams and buses in Kassel. But you need 2,75 hrs instead of 1,75 hrs.
There are direct ICE trains from Frankfurt Airport to Kassel-Wilhelmshöhe. A station on the periphery of the city. Kassel Hauptbahnhof (Hbf) the (old) central train station is only served by regional trains. Or you use a tram from Wilhelmshöhe.
map Kassel with public transport
kvg.de/fileadmin/kvg/dokumente/Plaene/KVG_LN…
DB timetable
http://reiseauskunft.bahn.de/bin/query.exe/en
From: FRA
To: Kassel
If you like to use the Hessen-Ticket select as means of transport "only local transport"
