So caught the Black Friday ad at Sportsmans Warehouse, and couldn't turn this down. Picked up a Savage Rascal for my kids to learn on (oldest is 5 now). He has a little ways to go before I think he's ready to handle the responsibility, but rifles don't have an expiration and I can put it in my safe until then. My only regret is I didn't buy an extra for me to turn into a fun pack rifle project. $130, how'd I do?
Rules followed, pic of rifle:
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Did good.  IMHO, putting a red dot on it is a good move.  Kids that young are still working on getting all of the mechanics down at the same time - holding still, sighting, breathing, trigger pull, etc..  Leave irons for a bit in the future when they've put the other things together.

I got one for my oldest when he was just three.  Even at that age, with me holding the rifle and him sitting on my lap, he could use the red dot and pull the trigger and do a not-so-terrible job of hitting steel plates, better than I thought he would do.

Since I started my kids out so early, I got the wood stock and chopped some off of the butt to help them shoulder it better.  It looks like a toy, but it's a very nice and fun shooter!

I'll second that adding a red dot and removing the rear sight is the best way to introduce your kids to the joys of shooting. As stated above, the red dot allows the kid to actually hit the target and have fun! They get frustrated very quickly with iron sights as they have to worry about sight alignment, stock control, and trigger control. With a red dot they can focus on stock and trigger control which is very important. They can learn iron sights after they get good at steadying the rifle and squeezing the trigger without jerking it. The old mindset of "irons before optics" is actually prohibitive to young shooters that lack the patience and fine motor skills that you and I have as adults.

I used the DI Products Rascal Rail. I used a Dremel to remove the rear section of the rail and mounted the red dot on the forward portion. This left the ejection port unobstructed so that loading is as easy as with the irons. We used a Weaver Micro Dot sight which has been more than adequate for the Rascal.

Here's the master hunter with his weapon and favorite target: