(Our messages crossed. Sounds like you've got it.)
I would recommend the 4-wire LED strips (APA102 style) over the 3-wire WS2812 style.
Pick a vendor. I bought mine from
these guys, but the exact item that I bought is no longer available. It seems like the current listing that's similar is
this one.
You can trim the strips at any number of LEDs and join them with 4 wire connectors of your choosing (or solder bare wires). You can run them all in a single string or have multiple strings. You can't really have strings that "branch" in the middle (you can, but don't, because then you can't control each branch independently).
I also bought
4-pin cable and the
4-pin LED connectors (but you could use any 4-pin connector or no connector as above). The connectors are the hardest and most time-consuming part of the project (and are the most fiddly, especially in a costume scenario where people are moving and flexing everything).
Then, get whatever Arduino suits your fancy. I used
Nanos. I bought relatively expensive
IR receivers. The cheaper ones did work in testing as well, but those are the ones I used for the costumes.
I find that the IR is plenty forgiving in terms of aiming. The kid(s) will handle it just fine. It's not like you need to be a sniper to hit it. Buy whatever IR remote control you want from whatever LED listing you want. They all work about the same.
This one is cheap [you're only using the remote portion of for this project].
Do us both a favor and start out with the IR remote (because I know it works and have all the code already written and proven on my stick figure costumes and it's cheap). If that turns out to not work well enough, I'll try to get the RF to work in the project.
You'll need a computer with the USB serial port driver and the Arduino software (free) installed and a cable to connect to the Arduino and a power supply to run the dollhouse. (A USB wall wart will work just fine.)
That's about all I can think of for now. Fire away with any other questions. I try to get onto EEVblog every day except when I'm traveling.