I'll admit I'm quite novice when it comes to judging peripherals, so I went with pretty much the cheapest full size mechanical keyboard they had listed. Unfortunately PCPartPicker doesn't seem to have any mechanical keyboards in close to equivalent pricing listed for NZ.

Given the pricing and that it's for kids, the cheapest from a brand you recognize will probably be fine. I don't know that spending more money will make much of a noticeable difference until you spend quite a bit more money. In my opinion, a lot of it is just personal preference, like the keyboard size/layout, wired or wireless, backlit or not, any extra shortcut keys, things like that.

For the mouse I went with what I recognized as a frequently cited best cheap/budget mouse. Something like this might be the closest available equivalent. Again, I feel like a lot of it comes down to personal preference. I don't know that it will matter much in your use case, but I know people look for things like high DPI, high polling rate, light weight, being able to switch DPI on the fly, additional buttons. Trying to stay within the equivalent budget of what I selected before, again I would say the cheapest from a brand you recognize will probably be fine, you're not going to get many bells and whistles without spending a fair bit more.