Booking train tickets in October - Austria and Germany

I rather doubt that a Bahncard would be cost effective for a trip with so few connections. It's really meant for someone who travels every day, What's more it is a subscription, which will renew every year until you stop it.

Are you flying into Salzburg on day one? Then you probably don't want to book a train-specific advance purchase "Savings Fare" ticket (the only advantage of booking in advance). If you have a day in Salzburg and can reliably make the train to Munich, then I would save money with an advance purchase ticket. I would use an advance purchase ticket for Rothenburg to Rüdesheim.

but i would like to ... not waste money.

Then my advice then is to not use first class. Yes, it's a little more luxurious, but unnecessary luxury, and, IMO, not worth the extra cost. Second class cars go precisely the same speed. You won't save anytime using 1st class.
Everything else are local tickets; no advantage to advance purchase.

Do we want a Bahn Card or??
The BahnCard 25 costs €19.90 and gives you a 25% discount on flexible and saver fares. To save money, you must spend more than €79.60 on tickets (for one person) so that the 25% savings is greater than €19.90.

If you're purchasing 1st class tickets, your two most expensive tickets (Oct 3 and Oct 7) could exceed €79.60, depending on which specific train times you choose. If that is the case, buying a BahnCard 25 would save you some money. In second class, your tickets are less likely to exceed that amount, again depending on the specific train times.

When you purchase a BahnCard, they mail it to your home in about 2 weeks. You'd want to order those (1 per person) quickly. Alternatively, you can also print the pdf version (which you will receive via email upon purchase) and bring it to show the ticket checker.

Also, if you want to show your tickets (and BahnCard, if you buy one) electronically, create an account first on Bahn.de and buy your tickets and BahnCard while you are logged in. It will simplify things when you download and log into the DB Navigator app where your tickets will be displayed.

From what I have read, to use a Bahn25 card on first class tickets you will need a first-class Bahn25, which costs around €60 versus €19.90 for second-class Bahn25.
If those are your only trains, the card seems like a bad deal. There are regional day tickets for some of your trips which are inexpensive -- and don't benefit from Bahn card.
Take a look at bahn.de/en to see schedules and costs of trains and book in advance.

I don't think either that buying a Bahncard is a good idea since it would be useful only for your two long distance legs. Moreover, if you forget to cancel it (six weeks before expiration at the latest) it will turn into an ongoing subscription! And I wouldn't spend the money for first class either, since almost all of your connections involve large legs on locals trains, where the difference between first and second class is neglegible and the number of first class seats is often extremely limited.

My suggestions (prices 2nd class and for all of you):

Oct 3
Either take the combo of RJX (Salzburg - Munich) and ICE (Munich - Nürnberg): travel time 2:53, €119.60 saver fare (if booked today; prices may increase; add €4.50 pp if you want reserved seats). There is also a first class (non-refundable) Super Saver Fare ("Supersparpreis") available for €159 including seat reservation.
Or take a combo of local trains (dep 11:15), travel time 4:35, €46 with a "Bayern Ticket" (price will be stable).

Oct 6
Rothenburg is within the Nürnberg transport area (VGN) - for four adults you'd need two "Tagesticket Plus" (20.30 each; if two of the travelles are children they can be included in the first ticket at no extra cost)
Trains run hourly at minute 21 past the hour; two easy transfers in Ansbach and Steinach (avoid time consuming connections via Dombühl). No seat reservation possible (or necessary).

Oct 7
The 2nd class saver fare is €111.60, route is via Steinach - Würzburg - Frankfurt. Travel time 3:58 when using the IC(E) between Würzburg and Frankfurt (€111.60 saver fare) or 4:58 when taking only local trains (€68 with an "Quer durchs Land" ticket)

Oct 10
Use a RMV group day ticket for €16.60

Oct 12
Use a RMV group day ticket for €16.60

Look up details for connections and fares at www.bahn.com. To compare fares involving long distance trains with "local trains only" connections do two searches and select "only local traffic" for the second one. And don't foget to indicate the age of all travellers: if two of the travelers are children up to 14 yo they travel for free.

This is just the advise I needed. Thank you so much. I won't bother with 1st class as it does seem like a lot more money that isn't necessary.