Emerald is the one I always find myself going back to. It and FireRed were the first games I got as a kid that were mine and not shared with my siblings, then we all traded and battled each other with our respective copies.

If you want to genuinely get into the series, my recommendation would be to start with FireRed/LeafGreen. The only difference between the two is that there's a few Pokémon only in one version to incentivize trading with someone with the other version. If you aren't going to use cheats, I'd look up which ones are the exclusives and pick which based on that.

After completing that game to whatever degree you consider complete, you've got a couple options. Personally I'd go Emerald, because nostalgia and it's the same graphically as FR/LG, but an argument can be made to skip it and go to HeartGold/SoulSilver next since its a remake of the second generation much like FR/LG was a remake of the first generation.

Now if you don't care about graphics and your main goal is "I want to complete the pokedex" and you also don't want to use cheats, or trading, the best option to go with is Yellow where you only need to worry about 150 Pokémon (I don't think Mew is available but am happy to be wrong)

This comment is getting a little long, but the last thing I want to shout out is PokeMMO. Its not affiliated with Nintendo/GameFreak in any way, is available on all OSes, all you need to do is get ROMs of a few games and it let's you move between the different regions and has increased difficulty over the original base games as it isn't directly targeted at kids. You can start in Kanto with the FR/LG ROM, do the story, then move to Johto afterward and so on, its a lot of fun, but I do think its geared more toward fans of the series rather than just people who want to play a game, but I'd still recommend looking into it.