Standard fare tickets are valid for any train of the same or lower category on your travel day and the following day while discounted tickets limit you to one particular connection, if you miss that train the ticket is lost. You never know whether your plane will arrive on time or delayed. After an intercontinental flight I'd bite the sour apple (German saying) and book standard fare tickets, then hop on the next train you'll reach.

Check with your airline if they offer Rail&Fly tickets, which are as flexible but a lot chepaer than standard train tickets. If they don't, buy standard tickets via www.bahn.com (avoid Raileurope or any other agency).

Seat reservations are not compulsory but nice to have - I'd book those for a train about 1.5-2 hours after scheduled landing time. If I catch that one, fine, if I take a different train, there is still the option to either book last-minute reservations at the station or simply hop on and look for a seat.