I never had an Atari, but I did get a TI99/4A (TI as in Texas Instruments) for Christmas when I was about 5 years old. That thing was my introduction to home video games, and set me up for a life of fascination with the hobby. It was a cartridge based system, like the Atari, but it also had various peripherals you could acquire, like a Speech Synthesizer and a built-in keyboard. It also came with 'Basic' built in, and my dad at one point gave me a book on programming in Basic when I was roughly 8 - he likely figured it was cheaper than buying video games themselves. That is largely what got me into programming and a deeper understanding of computers and video games beyond the controllers and cartridges and was the foundation of what I would apply to my MUD - Kingdoms of the Lost - over a decade later.
Anyway - I'm rambling a bit, but I may call back on the TI99/4A, since when it comes to game reflections, it doesn't get any more retro for me than this. The two games I wanted to touch on briefly were TI Invaders and Munchman. Basically - Space Invaders and Pac-man remakes, but in some ways, a bit deeper than their originals.
TI Invaders works much like Space Invaders - you have little aliens in descending rows with the occasional UFO passing by over top of them, while you are a tank, using destructible barriers for shelter in between your shots to fend them off. This was not my favorite game for that system, but I did spend quite a bit of time playing it. I don't recall what the highest level I got to was, but I do recall I was better at it than my dad. :)
Munchman was a similar to Pac-man: you have mazes to wind through, while avoiding 4 enemy characters that attempt to collide with you. There are 4 power pellets in opposite corners of the screen. Eat them, and you can then eat your four wandering assailants. One thing that was different about Munchman was that the 'ghost' characters actually took on several different shapes with each new stage (if I recall properly, there were 20 stages in all before it looped back to stage 1). Also, instead of eating pellets you created a chain-link behind yourself. The objective was to fill all of the passages with the chain link. A couple of variants included a level (7 maybe?) that had invisible walls, making it much harder to get away from the 'ghosts'. I think the last level, or near the last level, you were eating things instead of making a chain. When you 'eat' the 'ghosts', you make a small burp sound. This game, I had gotten good at (and had cleared all of the levels).
There is an emulator out there for the game system (it's one of the few systems I actually don't still currently own) - and it includes several first party games (but none of the later-released 3rd party ones like Moon Patrol or Donkey Kong). What's awesome about this emulator is Texas Instruments approved of the creator including several of their games, like the two shown here. If you're at all interested, I found his page here. I was just mucking around with a keyboard and not a controller, and I was obviously struggling with some of the default key bindings - so I stunk it up in quality fashion in the embedded video below. But, take a look and I hope you enjoy taking a peek at some of my very earliest gaming memories.