Trees and scratchers are a must, cats usually scratch furniture because there isn’t something else nearby to use. Trees give them a place to climb and feel safe up away from things. You should also have places for them to hide (boxes, piles of blankets, a bed in a quiet room, etc). As for toys, it really depends on the cat. Ours is super picky and only likes specific rattle balls from Amazon, small rattle mice, and some kickers (there are few others but they are all small and easy for her to cray around). But for every one toy we found she likes we have half a dozen she won’t touch. You’ll likely need to try a bunch to find what yours will enjoy.

Cat tree is a must to give the cat a place to scratch without damaging your furniture.

I found that little mice work best as toys for a young cat, he can entertain himself with them but over time lose interest. Toys on strings work universally well, and let you interact with the cat.

It may be a good idea to install some shelves so your cat isn’t limited to floor and furniture, and can explore your home vertically as well.

Make sure to get at least one scratching post. It’s much better than waiting for them figure out which furniture makes a good scratching post.

Cardboard box. Not a joke. This is famously the most universally enjoyed object for cats.

So I know this is a thread about toys, but it looks like you got a lot of good advice, and since you’re new to cats, one thing that most people either don’t realize or ignore is the number of litterboxes. 1 is not enough, even for a single cat. General rule of thumb for litterboxes is Number of cats + 1. You want them to view the entire place as their territory and a big part of that is scent markers. And the biggest of them is the litterbox. Many cats will, as soon as you change the litter, use it. That’s because they want it to smell like their territory (To their sensitive noses). Spreading that around for them makes for a happy cat and reduces the chances of “accidents” or just marking territory later on in times of stress.

I’ll also say you should probably have a scratching post on every room that they hang out in regularly. They’re not going to go to another room to find it if they want a good stretch or scratch. I suggest angled or flat ones at first because they will often use them to really stretch out their spine so they need to get a lot of distance between stretched out back and front feet. That’s a lot easier (and cheaper) in flat or angled ones. If they end up preferring upright ones they got to be real tall to give them what they want. And those are expensive.

One more tip. Even if you decide to feed them dry food, use designated feeding times. Read the package and figure out how much they should eat a day and split that in 2-3 parts and measure that out giving them meal times. It’s better for their physical health and it’s more in line with their body’s natural rhythm.

In general though, it’s best to establish routines for behaviors you want to promote (Cats love routine) early on and keep it up. If you try to introduce new routines later it’s a lot harder to establish. The change of moving into a new home is the perfect time to create a new routine since everything is kinda chaos for them anyway and it helps them establish order in their lives.