John,
As Julie says, be careful about what you give to pets for treats because some have allergies and owners tend to be a bit hyper about them. I suggest they bring their favorite treat when they come.
I have a bunch of squeaky toys that can be tossed plus I use tennis balls that can be rolled for dogs. The only problem is that the dogs tend to chase them

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I also have a few that emit strange sounds when you press their paws so I have a wobbling chicken, a burping Aardvark and a hedgehog that makes very rude noises.
I've developed my key mouth noises for all types of pets which include a ping pong ball, horses trotting, and various other noises not usually permitted in polite company

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My "standard" baiting food is milkbones. Right out of the box. Most dogs recognize them and look at them when you hold them up and you can break them in two for quick treats. And most owners are fine with them. The head shot I posted of Blue was gotten when I held a milkbone in my left hand and just moved it from my far left to my far right. He closed his mouth, and just followed the treat with his head and eyes.
That's another thing -- open mouths. Most dogs will start panting when they've been working for a while under the lights so you might want to get a spay bottle with some water and a little bit of lemon juice to squirt in their mouth when they won't put that tongue back in.
Don't forget the grooming stuff as well -- brushes & combs to get that coat nice and shiny before you shoot. For both dogs and cats. I've also found that if you get a small spray bottle of human leave-in conditioner (I use Herbal Essences), you can spray that on the coat and brush it out and you not only get a nice shine, you get a lovely scent. You're on your own with birds.
I've found that if somebody else can get the pet's attention, I can just toss a toy where I want to get them to look. That is the best combination for me.
Have fun. It's all about learning and keeping the shooting environment as relaxed as possible.
Jim