Italian Dolomites advice

Hey! The husband and I are going to the Italian portion of the Dolomites for our honeymoon at the end of September/beginning of October. This is our first time doing any sort of trekking trip (: Life is busy and we’re a little bit late in starting to plan. We can always take an Airbnb and do day trip hikes, but we really want to do hut-to-hut. I’ve found a bunch of companies that plan everything for you (currently looking at Mont Trekking), but I’m assuming that’s super expensive versus booking your own huts. Anybody have experience with this? Should we try to book on our own, or are the companies that do this for you worth paying for? Or is there not that much of a price difference at all?

Thank you!