For an afternoon flight out of FRA, in the past I've come in from near Karlsruhe (Bad Herrenalb) on a direct ICE, from Boppard, on the middle Rhein, on a direct RE, and from a small town ½ hr west of Würzburg (direct RE to Frankfurt Hbf, S-Bahn from there). I've never had a problem with connections; the German trains are reliable. Because of the time, I've always allowed extra time for the trip and used it for lunch at the airport. I would avoid coming all the way in from Coburg because of the uncertainty of connections.
There are hourly, direct ICE and IC connections from Würzburg direct to the Fernbahnhof at FRA.
For a morning flight, I've always (3 times) stayed next to the Hbf in Mainz. My last stay in Mainz was here, at Hotel Königshof. Königshof is a nice hotel with rooms reasonably priced for so close to the airport. It is right across the Bahnhofsplatz from Mainz Hbf, a very short walk in the morning. They serve a great breakfast buffet, including a table of traditional American breakfast dishes, if you care. The trip from Mainz to the airport takes 27 minutes and runs every half hour.
Some people have complained about noise in the Bahnhofsplatz, but I didn't notice any.