i would personally start with the Connection v3. It improved upon the v1 and v2 (more games, food, and characters), but the gameplay is still simple and easy to understand. It's a great starting point, since it's easy yet fun. They're fairly inexpensive, too.
After that, you would have a fairly solid basis for any other Tamagotchi. You could get a Connection v4/v4.5 (which adds careers your Tama can get and even more characters), a v5 where you raise a family, a v6 where you train your Tama to become a music star, or even a color version from Japan (probably ID L or P's, since they have the most features). I personally would recommend playing one more of any of the Connections I mentioned before buying a color version. The color ones are in Japanese, but they're pretty easy to understand if you're familiar with the Connections.
So, in short: Get a Connection v3, then a Connection v4/4.5/5/6, and then a color ID L or P's.
I hope this helps! Let me know if you have any questions.