Do you have enough cold weather so that your peony foliage/stems turn brown and die back? If so, I'd wait until you see them browning. If you don't I'd go ahead and cut them back to try to push them into winter mode. They do need a month or two hibernating for all of that spring growing!
The Itohs I have act just like a normal herbaceous peony in their habits although you'll probably see eyes at the base of this year's stems rather than all from the ground. In my climate those buds don't make it, sadly, but you might be warm enough for them to survive. If you do see those eyes just leave a bit taller stem, a few inches rather than just one or so. Don't worry if you don't see those stem eyes though, some Itohs do, some don't have them.

The weather has been warm with lots of rain. I left about two inches an also see some eyes. Will I see flower next year?

I have seen 2 Bratzella peony plants in the local nursery.

one with stem with few eyes on it (like tree peony), one with ground level with more eyes on it.

If I want to buy, which one is best choice?

Raindrop, it's hard to predict if you will see blooms next spring, depends on how big the root was, how deep it was planted, how well it likes the spot you planted it and how lucky you are! Itohs are supposed to be more reliable bloomers than some of the herbaceous for the warmer climates so you have a good chance. If you see multiple stems growing in your early spring I'd say probably. If you only have a few, probably not. Lots of growers say not to let them bloom first year, to pinch out the buds to allow the energy to be spent on roots. I'd say if you get a lot of buds you might want to pinch most out to minimize the chance that the newly planted roots don't have enough energy to make it all the way to opening blooms.

Bunti, the stems die off here like herbaceous, I'd say the one with more eyes. Just make sure it's not rootbound or if it is you might want to divide it before planting. Be prepared though, you might need a coping saw instead of just a knife!