Handheld Retro Gaming consoles - are there any experts in the crowd?

Personally I would go for RG350M, but it doesn't meet your requirement to have icons instead of titles to choose games. It is also much more expensive.
X12 Plus seems to be very reasonable choice, but you may check also JXD 5" S5110b as it is only slightly more expensive than X12 Plus.

https://www.goretroid.com/
https://www.youtube.com/watch?v=c25Z8xZS4gE

I used to have an archos gamepad, so an android tablet with joysticks, but after a little fall on the carpet it became slow, they had another faster one later, but seems they are no longer for sale.

You got these programs where you can scroll through f.e nes and you see all titles and screenshots, then your kid can also easily pick or say hey this looks cool. just don't put too many on them if they can't read.

The psp and ps vita are supposedly amazing retro emulators. And a good interface is a given with these ones.

I'd recommend getting Playstation Portable, it has excellent native PS1 emulation and tons of homebrew emulators for every major console. Installing custom firmware that allows to run homebrew may be a little tricky. Plus, there are lots of native games of excellent quality.

It is sturdly built and has one of the best responsive D-pads I've ever encountered. I think PSP isn't manufactured anymore, but there should be no problem in finding it used or refurbished. Seek for PSP 200x or 300x models

I follow a great youtuber that plays some of these portable consoles and his favorite is bittboy, is cheap and emulates these old gens handled gameboys from 2000-90's, if you have a interest for a really good emulator and project search for recalbox.

My sincery opinion: i prefer play handle games on portable, home consoles emulated in these devices , on handle emulators is not good for me.

https://retrododo.com/retropie-handhelds/

There are just very many routes you can go through with it and not one really sticking out as the best. ;)
Old psp/vita would be best but gonna be hard to find (cheap).

Raspberry is very powerful depending the version you get and thus emulate a lot more, but you need that, a sd card, and a case, while it's nice to build something with your kids, it isn't exactly lego, so if they break something...Just let them watch and keep the raspberry in the case at all time.

I done something like this with my Raspberry (i got like the red one but for 1 player) https://www.youtube.com/watch?v=psWCmLwvWBE
Although i still can't get it working properly (sound and joystick) as it's based on linux which i am not good at, and again time (and so many consoles)..You can buy kits for it online if you aren't handy to make it yourself, but if you buy a kit you also looking at 200+.

I was on the lookout for a handheld like this a couple of years ago.

In the end I decided to get a second hand PS vita (100€). I don't regret that decision.

You can play vita games, psp and ps1 games through adrenaline, remote play from your PS4 or PC (if you have a GeForce gpu) with moonlight and a bunch of emulators, including retroarch and pFBA.

This year I also got a new 2ds (also 100€) and I would say that console is a child's dream. You can flawlessly play SNES, GBA and DS on it and emulate a couple of other systems, as well.

https://www.youtube.com/watch?v=RxEh_aJEAWc pricey but very very powerful. :p