Which product(s) should I buy for basic project (described in body)

Hello! I would like to create something whereby if I have two small wireless objects, I can push a button on one and doing so will make the other one light up. Can someone please guide me in what Arduino product(s) I should start with?

Thanks in advance!

Well, you could do it with two HC-05 bluetooth modules and any Arduino you like, which means you might as well use a Uno. I rather feel you can do what you want without using any Arduinos.

Cheap 433MHz keyfob with receiver module that has pins going high. I have a few of these where the receiver has 5 controlling pins, 4 go high based on which 4 buttons are pressed and 1 that goes high when any are pressed. It was probably a couple bucks on ebay.

Look for something like this

You can always remove the remote innards to fit your project. Make sure the receiver has those 7 pins. This works all by itself, no Arduino needed.