Which airport would you pick?

Are there any direct flights from your home airport?

Yes to all three

Really not a lot of difference between the 3. Swiss is part of Lufthansa, for what it's worth.

Zurich airport is a bit smaller, and closer to the city. Munich is a bit away from downtown.
Frankfurt is big and more spread out, there is a new Terminal 3 that I cannot comment on.

All three are easily accessible with public transportation and have plenty of dining options.

People have variable comments about every airport with the EES snafus these days, but
I would say Zurich and Munich are a bit more efficient and easy to get around than Frankfurt.

So I'd probably look at airfares going into each city and use that as a major criteria.

If Switzerland, we like to stay our last night in Glattbrugg, at the Premier Inn, Glattbrugg. On the tram line, 2 stops from the Zurich airport. If Germany, we like to stay in Neufahrn at the Gasthaus Maisberger, on the S1 train line, 2 stops from the Munich airport. Maisberger is more traditional, better food, for a last big meal.

If flying into either one, both have easy train connection to the hbf. in the city.

If flying into Switzerland, the ATM's will have CHF, good only in Switzerland, the other two cities will have Euro, good everywhere else.

Most probably depend on nonstop flight and airfare. We’ve been thru all three.

Does it need to be a ”loop”? Depending on where you are going, a multi-city ticket might be more efficient (e.g., fly into Frankfurt and home from Zurich).

Otherwise, I prefer Zurich or Munich over Frankfurt.

I’ve only taken Swiss and Lufthansa on intra-European flights (my overseas leg is usually United) so can’t speak to any differences. I’d perhaps look at type of plane and seating configuration.

People have reported that Germany still stamps passports, which is an added step beyond the EES fingerprinting and photos. I don't think Switzerland is doing that. But if you enter via Switzerland and exit via Germany, they will probably be asking where your passport stamp is.

We need more information. Are you going to take buses, trains, or rent a car? A rental car will significantly increase your costs. I would either start in Zurich and leave from Munich, or start in Munich and leave from Zurich. I would not go out of Germany and then back into Germany. I would do one country and then the other but I don't have a definite reason but it feels best. Frankfurt am Main has the busiest airport. I would start planning by tentatively avoiding leaving or arriving from Frankfurt. Your actual final itinerary should depending on the costs versus the times the planes leave and arrive versus the lengths of layovers. I arrived in Munich and left from Frankfurt am Main. I didn't make time for any of Switzerland. I took the trains. Also factor in the costs and length of times of train or bus trips. Frankfurt am Main's airport is big and takes too long to navigate. This only matters based on other factors. After you make up a tentative itinerary, keep checking prices of other options until you are sure about your itinerary or until you find better options.

Don't do a loop as you originally imagined.

I pick my airports based upon where I am going and my airline status, including access to an airline lounge. I always spend my last night before travel at an airport hotel, so transportation is never an issue I consider. Since your plans are to visit all three in any order and which airline doesn't seem to be a criteria, I asked Google which of the three is the most punctual.

Zurich Airport (ZRH) ranks highest among the three for on-time
departures and arrivals, followed closely by Munich (MUC), with
Frankfurt (FRA) consistently trailing in third place.

It would depend on the airline, flight times, convenience and price.

If all three airports are equal in the above, I'd choose Zurich. I've always found that airport easy to manage although the walk from gates can be long.

As of now, Germany does like to stamp passports. If you enter via Zurich, and they don't stamp, this flusters the Germans upon exit. If they can't find your entry stamp, they may ask you to prove when you entered Schengen. If good, they will then stamp your passport on exit. (They will also tell you what countries no longer stamp and let you know they are not happy about it.)

This happened to me. Just be aware.