First time in Germany

I assume Munich to Paris needs to be bought/reserved ahead of time,
but would welcome any advice on the best way (or website) to do that,
hopefully on a high speed train.

Correct, buy the tickets from DB, www.bahn.de. They can also be bought from SNCF, www-sncf-connect.com, but DB's site is easier to use.

All destinations are in Bavaria (except Pairs) and can be reached by regional trains (RB or RE, no IC / ICE), so have a look at Bavaria ticket. No train reservation needed at valid day - you just take the train which works fine for you.

For Paris ticket use https://int.bahn.de/en - and book as early as possible. Prices only climb.
If you are fine with night trains also look at https://www.nightjet.com/en/#/home.

I also recommend the Bavaria ticket if traveling around Bavaria. Have you considered Salzburg as a stop? Also covered by the Bavaria ticket.

Thank you all for the help. And yes, we're thinking of a day trip to Salzburg during our three nights in Munich. Anything specific to know about that trip?

“Anything to know about Salzburg?”

Your trip to Salzburg will be awesome!

Usually I plan my itinerary with the utmost care, but didn’t for Salzburg and still loved it! I like the Sound of Music, but was skeptical about Salzburg being a one trick pony for Sound of Music fans. However, it is much more.

We headed to Mirabelli Gardens, crossed river towards Getreidegasse to see Mozart birth sight, and then headed up to the Hohenslazburg Fortress, which is awesome, itself, and has an amazing view of old Salzburg on one side and the Alps on the other. Then we descended from the Fortress and saw the main cathedral and saw Mozart Square too. Ate at Zwettler’s Wirsthaus. All on foot with 4 kids.

Enjoy!

If you visit Salzburg, also visit nearby Berchtesgaden.

Further, from Munich, you should visit Garmisch and Fussen near Austria. Go up the top of the Zugspitze and of course see the castles.

Also, Augsburg is worth a day as well as going up the Romantic Road.
https://www.romanticroadgermany.com

This website (if you don't already know it) is great for general over view: https://www.seat61.com/train-travel-in-germany.htm
He does try to keep it up-to-date, but as always with websites, go to https://int.bahn.de/en to check timetables and current ticket price.

I saved quite a bit of money on a cross-border train originating in Germany this summer by buying early - a Super Sparpreis fare. I booked as soon as the train we wanted became available. You are locked into the one train booked, but at the fare I paid, if we'd changed our minds we would have not lost much.

People above have noted to use the bahn.de site. That is important - when you google, you are likely to get Rail Europe or Trainline - agents. You don't want to buy from them - go to the source.

One other hint - especially if you buy early. There was a change to one of the trains we took this summer - change in departure station, of all things. Somehow, I didn't get notice of that either by email or on the train app. I did have a bahn.de account but was told that sometimes the Deutsche Bahn system isn't good with updates. Luckily for us, I checked on our train via the app the night before departure and saw the change. So, lesson learned, in future, I will monitor my booked train departures in the same way I tend to monitor my airline departures.

Again, many thanks all! Such helpful info. I'm guessing my Munich > Paris tickets can't be purchased till maybe 60 days in advance. They don't seem to come up yet on the DB site. I'll keep trying.

Just want to double check one thing: we land around 1:45pm in Munich and will hop right on a train to Regensburg. We can just buy these day of at the station, yes? Or is there any benefit in purchasing in advance? We will have had a long journey from Nashville and are happy to reserve seats on the train if that's even a thing on these shorter regional trips. Thank you!

Best is to take the direct train to Regensburg (line RE 22). Alternatively, you could use a bus / train combo via Freising. In both cases get a Bayern ticket either at the ticket window in the MUC Airport Center or at a vending machine (2€ cheaper) or download the DB Navigator app and book it there. Pre booking has no advantage . There is no seat reservation on regional trains.

I'm guessing my Munich > Paris tickets can't be purchased till maybe
60 days in advance. They don't seem to come up yet on the DB site.

When are you travelling? If it's after the schedule change on the 10th the tickets will not be on sale until the new schedules are set, which can take a while. So just keep checking.

There is one daily direct TGV from Munich to Paris, as well as a number of options with a change in Stuttgart. Due to bureaucracy the departures with a change in Stuttgart are actually faster than the direct train.