Train tickets from Frankfurt Airport to Rothenburg with a stop in Wurzburg

I did the exact thing 2 years ago; you can travel on any train on the Wurzburg to Rothenburg ob de Tauber route and you don't need to buy it in advance as it is 2 RE trains at a fixed price; it will go: Wurzburg to (change in Steinach) to Rothenburg ob de Tauber

If you advance purchase Savings Fare tickets, they are only train specific for long distance trains (ie, ICE/IC/EC), which you would use for FRA to Würzburg, so you could stay in Würzburg for a variable time and continue on from there to Rothenburg, which is by regional train. However, I would not recommend using a Savings Fare ticket from Frankfurt airport. If your flight to Frankfurt airport is late, you could miss the ICE to Würzburg. Your ticket would become invalid, and you would have to buy a full fare ticket to Würzburg.

Alternatively, you could take the S-Bahn from FRA to Frankfurt(M) Hbf and catch the regional RE from there to Würzburg via Kahl am Main, the first stop in Bavaria. An 8,35€/P local RMV ticket will get you to Kahl; a 31€ Bayern-Ticket (assuming 2 of you), purchased at FRA, will take you the rest of the way to Rothenburg. You don't have to change trains in Kahl, just tickets.

If your arrival is on a Saturday or a Sunday, you can use a Weekend Ticket, which is 40 EUR for the first traveler and 4 EUR for each additional traveler up to 5 traveling together. Regional trains only, and buy from a ticket machine at the Regionalbahnhof at the airport. Costs 2 EUR more if you buy at the ticket window.
https://www.bahn.com/en/view/offers/regional/weekend-ticket-for-germany.shtml?dbkanal_007=L04_S02_D002_KIN0060_REGIO-INDEX-SWT-OBEN_LZ01

Below are some tips to elaborate on the advice above (apologies in advance... it's a little complex.)

First thing... I know nothing about the rest of your itinerary, but it's possible that some kind of German rail pass would be useful. The rail pass is particularly helpful for those traveling right after a flight since you can use ANY train, regional or long-distance/high speed, at any hour. From FRA there are DIRECT high-speed trains to Würzburg that take only 1.5 hours; the regional trains will require 2.3 hours. But for now let's assume a rail pass is out of the question for whatever reason...

Trains from FRA to W'burg: Agree that without a rail pass you need a regional train option for this journey. The "RE" Jazz+ mentions stands for "Regional Express" - the faster of the regional train options. From FRA however, you will need to board the milk-run "RB" train into Frankfurt's main station and change there for the RE train to W'burg, as Lee has outlined. The tickets Lee suggests (RMV + Bayern Ticket) should be purchased at FRA's Regionalbahnhof (regional train station, one of two airport stations) where you'll find ticket machines like these. There is airport signage to guide you to this station.

Trains from W'burg to Rothenburg: These will be RB trains - one change of train in Steinach. The Bayern Ticket you used to reach W'burg continues to cover this part of the journey.

One possible caveat for the Bayern Ticket: If it's a weekday, your Bayern ticket will not be valid until 9 am, which means that the earliest train sequence you can use is the one (current schedule) leaving FRA at 8:02; your 2nd train out of Frankfurt's central station will leave at 8:34 and pass through Kahl (where Bavaria begins) at 9:03. That and any later departure from FRA will work just fine.

How to find the regional train schedules: They won't just appear automatically at the DB itinerary search page. You must check the "only local transport" box under "CONNECTIONS."

Luggage: Würzburg has station lockers while you sightsee.

Suggestion: If you are arriving at FRA after a red-eye international flight, spend your first night in Würzburg. You are likely going to be bushed/jet-lagged that day; you'll want to do a minimum of luggage-tugging and train-hopping.. a hot shower and dropping your bags off for good might sound very appealing. Also, Würzburg is a very nice place to sightsee and to stroll around and to just get your bearings. Seeing the Residenz and the adjacent Hofkirche will take some time. There are other things to see/do that you might wish to make time for if you have the energy. Go to R'burg the next day. If you take this suggestion: There's a two-ticket regional option to Würzburg... RMV ticket from FRA to Frankfurt Central (€2.90 ea.) + a "Regio-ticket Main-Spessart plus Frankfurt" ticket (€28/1 + €8 per additional passenger) for Frankfurt Central to W'burg... so about €42 total for two. Buy both of these at FRA's Regionalbahnhof station, just like the others. On weekdays: the 2nd ticket is valid only after 9, so the earliest/best train sequence on a weekday would be the 9:02 from FRA airport (11:21 in W'burg.) On Sat or Sun the 2nd ticket is valid at any hour so you can leave FRA earlier.

Besides the train connections suggested above there are numerous Flix bus connections between FRA and Würzburg, the fastest in 1:40. Walk up prices start at approx. €17, details here. That alternative is worth considering only if you stay in Würzburg; for the Würzburg - Rothenburg leg you need the train anyway.

Strongly agree you should spend your first night in Würzburg. By the time you get there, you'll only have the rest of that one day to see what is really a nice place with a great deal to offer that deserves more than just a couple of hours. Since it does not take that long to get to Rothenburg, and your hotel wont be ready until early afternoon, you can finish up your sightseeing in W'burg the next morning.

Oh my goodness!!! All of this information is so valuable and I can’t tell you how much I appreciate the input!! You all have made some wonderful suggestions and set my mind at ease!!
Thank you again!!
Shari

When I saw that you’d written “a couple hours” for Wurzburg I frowned. I agree with others that if you have the flexibility, make Wurzburg an overnight and give yourself a day to 1.5 days to really enjoy it.