How many people are traveling in your group? You already asked about the Tages Ticket Plus, and this is good for up to 2 adults and 4 children under 18 years old. So that is the cheapest deal if there are at least 2 adults. It will also include public transportation in Nuremberg from your lodging to Nuremberg Hbf. As said, buy from a vending machine or use the VGN app.
Regarding your planned connections:
RE 90 originates at Nuremberg Hbf, so it is highly likely to depart on time. It makes only 3 short stops between there an Ansbach, so it is also highly likely to arrive on time.
RE 80 is a regional train that originates in Treuchtlingen going to Wuerzburg. It is scheduled to arrive in Ansbach before RE 90 arrives, and will be sitting there waiting for you. Note that almost all stops along the way are 1 minute or less, time enough for people to get off and new passengers to board. But in Ansbach, it remains in the station for 12 minutes. So that it is a hint that this is a designed connection for people coming from RE 90. Just be waiting by the train door with your luggage as RE 90 arrives in Ansbach and get off as soon as the train stops in the station.
RE 80 makes just 2 quick stops before arriving at Steinach. Again, be waiting by the door with your luggage as the train arrives at Steinach and get off immediately.
RB 82 is just a little train that shuttles back and forth between Steinach and Rothenburg. The trip is only 15 minutes with 2 quick stops along the way. Every hour it travels to Rothenburg waits there 15 minutes, than travels back to Steinach. So it can wait a minute or 2 for stragglers, as long as the conductor is aware of it. 90% of the people getting off at Steinach are continuing on to Rothenburg, so just follow the crowd.
