Well, from someone who was adopted by a 6-month-old tabby kitten approximately 2.5 years ago, toys are a must. A cat tree is also quite nice, because then you can use catnip (most cats love it) to “train” her to scratch and pick there and not on your furniture. We got ours from CL; a guy made it out of 4x4s and plywood covered with carpet, and it’s sturdy enough that our 55-pound hound can jump on it with no worries. Elinor loves hers, and while the acrobatics performed on it have been toned down a bit, she much likes sleeping in its various cubbies and perching on the top to stare out the window.
Toys … Elinor won’t touch it if it doesn’t rattle, so about the only thing she has are lots of rattly mice, which end up under furniture that she is now too big to fit under. A sweat scraper is great for retrieving them. A word about toys: you may want to keep them out of the dog’s reach until you’re sure he won’t eat them. One of our dogs ate a rattly mouse, which didn’t agree with him, and we had to take him to the vet to make sure it was progressing through his digestive tract and not getting stuck.
When we first got Elinor, neither of our dogs had been around cats, and they both thought she was food. One dog got over this pretty quickly and more or less ignores her. The hound, OTOH, was a freak about her for the first month, so they were kept separate (she was in her room when he was out; he was in his crate when she was out). As he started to deal with her better, he got to come out wearing a basket muzzle … I think about 3 months after she arrived he was OK with her. They are all loose in the house now when we’re home with no worries. In fact, Elinor usually plants herself in the middle of the huge dog bed and passes out, which causes some whining and angst between the dogs, who aren’t about to share the bed with her.
When we are not home, Elinor has a room upstairs (spare bedroom with elliptical and small cat tree in it) where she stays; she also goes in there at night, mainly because as a younger kitten, she had a penchant for chewing on power cords. :no:
I have always followed the litterbox rule of having one more box than you have cats, so I have two boxes for Elinor. One is a regular box and one has a top. She prefers the one with the top, but I wanted to do everything I could to be sure she used a litterbox.
We just put her in there and moved her front paws in the litter, and she figured out the rest on her own. (You may want to keep the litterbox away from the dog … some dogs think there is nothing better than snitching snacks from the litterbox.)
Good luck with your new house and your new kitten! 