The rapids are class III-, similar to the San Juan. There is one rapid in the wilderness section that is class III-, it's called Aragon and is easy to scout or portage if you don't like it, but it's not really difficult.
The daily section below the monastery has several class III- rapids, you get some good waves, but the river is pretty mellow. If you are worried you can shuttle to Chavez Canyon instead of Big Eddie and skip that whole section, but I find the Chama to be very mellow and a good place to have fun and learn on easy class III's with minor consequences.
Have a great time - that is a wonderful stretch of river!!