The problem with flying into FRA, and then taking a train to Munich is that the fare for fast trains (ICE/IC/EC) is quite expensive if you book an open ticket (usable any time on any train). There are advance purchase fares (called SparPreis) for considerably less, but these fares are valid on only one specific (date and time) train, so late flights will present a difficulty. If you advance purchase book a train for shortly after arrival, and your transatlantic flight is late, your would lose your non-refundable ticket, but if you build in a time allowance (how much is enough?), and your flight arrives on time, or even early, you could waste a lot of time waiting for your specified train.
One solution is to plan on spending a few days near Frankfurt, and see some things there before taking the train with the discounted ticket, when you know you can make the specified train, to Munich. I did this a few years ago. I was going to Bavaria (around Füssen) but flying into FRA. We railed down to St Goar, on the Rhine, for a few days before taking the long distance train (with advance purchase tickets) to Bavaria.
A second solution is to take regional trains from FRA's Regionalbahnhof with a Quer durchs Land Ticket (63€ for 4 adults). Regional trains will take you about 6 hours (vs 3½-4 hours by ICE), and you will have several changes of trains, but you can leave for Munich as soon as your flight arrives (and you buy the ticket). The QdLT is an open pass, always available for the same low price, for all regional trains in the entire country for a day (after 9 AM workdays, all day on weekends).
A third option, which is more expensive than the QdLT, but allows you to use faster, long distance trains, is called Rail&Fly. It is available with some airlines (Lufthansa is one) and includes a rail ticket coupon with your flight ticket that is valid on any trains of the Bahn on the day you arrive or the next day. I think you have to book it with the airline along with your flight tickets. Last I knew, it cost 33€/person, which is more than 16€/P for the QdLT but would allow you to board the next fast ICE to Munich after you arrived. Seat reservations would not be included at that price, but you could purchase them after you arrive.