I have the opportunity to go on a Friday in September to see the Cheese Market. Is this just a cheesy (too touristy) experience or is it worth the side trip from Amsterdam?
The cheese market as such is not worth the journey. It isn't much more than some elderly men running around with large cheeses and loads of foreign tourists making pictures of it. After ten minutes you have seen it all.
The city is nice though for wandering around the better part of a morning. After that you could do worse than continue to Hoorn (30 mins) or Enkhuizen (1 hr), both gems of historical cities. My favourite is Enkhuizen. To all standards (historical importance, city rights, monumental buildings, defence works) a city, but it feels like a village. You can easily fill half a day wandering around and even longer when you decide to visit the Zuiderzee Museum.
We thought it was worth the day trip for us in 2018. After we watched the “elderly men running around” as Ton says, please wander the streets away from the hordes of tour groups. There are fantastic cafes and boutique shops just a street away (Hekelstraat) from the cheese market.
I will be traveling by public transportation. Question to the people who recommended Enhuizen afterwards - were you driving or using buses/trains and can you tell me something about the latter public option?
Everything can easily and comfortably (no need at all to take 1st class!) reached by train. Use www.ns.nl (it has an English-language button) as your train planner.
It might cost you 1 or 2 euros extra for the service, but you can buy the tickets the day before at the manned window at Amsterdam Centraal.