I'm currently going through it now. Steel REALLY wants to play with the cats. He gets super excited and barks at them. Occasionally, he'll "catch" my male cat and mouth him a bit, then stand there like "why isn't he playing back?" I haven't had a puppy this focused on the kitties before and Katsu supposedly has a higher prey drive than Steel. It's definitely more of a "these are weird looking playmates" focus rather than "I'm going to kill that furry thing" focus. I had a cat killer growing up.
I was told to "make myself more interesting than the cats" but, imo, easier said than done, lol. I use "no kitty!" as a leave it for the cats and we're actively working on this command. It is a work in progress for us, probably 80% of the time right now. I'm doing my best to keep him from chasing the cats as well.
Depends on your puppy. Katsu got over it after a few weeks. The cats are indifferent to her. Steel, it's been 1.5 months and he is getting better, he's just taking more time in this aspect of training. If your cats haven't dealt with a puppy before, more likely than not, they won't be super lovey to her.
I have barriers (baby gates) up for the cats to have "dog free" places to go. During the day, they have free reign of the house. When I'm home, there's the laundry room, a bathroom, and a spare bedroom gated off for them if they want to be alone (typically they don't but will go there if the puppy is being too annoying).
I think a trainer isn't a bad idea! Congrats on the cute puppy, btw!