Best Way to Travel from Munich to Baden Baden

Cheapest - probably bus. Fastest - I would bet - train. I would go by train. Certain train tickets bought enough ahead are substantially cheaper. In that case train would be even cheaper than bus. For schedule and ticket prices check Deutsche Bahn website.

Train. The Deutch Bahn website is quite user friendly. Buy tickets online well in advance for the best prices (20-30 Euro to Baden Baden. 20 euroto Frankfurt, saver fares).

https://www.bahn.com/en/view/index.shtml

Thank you!

When you buy the tickets online, how are they delivered? Will call or sent to you electronically? Appreciate your guidance.

albertmuller, the DB website (as well as most European national railway company sites) offers an option of a "print-at-home" ticket, same as airline boarding "cards".
You get a confirmation e-mail with a PDF file attached. This is your ticket. You need to print out the PDF file and bring it with you (some companies allow you to keep your ticket on your phone).

When the ticket inspector on the train asks to see your ticket, you show this printout and your ID (passport). The ticket has your name on it (entered when you bought) and the ID check stops you giving a second copy to someone else to use.

history,

You might consider taking a Taxi from the Baden Baden station into town. As I recall, the station is a short distance from the main part of the city.

If you have a print-at-home discount DB rail ticket purchased in advance, you may be required to produce the credit/debit card that you used to purchase it.

or there is a bus from the Baden Baden station into the town.