Grab Blue/Red/Yellow from the 3DS Shop. It will have the most relevancy to Pokémon GO. 

Heres a few quickly googled pictures so that you have an idea how they look. Just in case you are turned off by the archaic visuals.

Pokemon Red/Blue:

Pokemon Yellow:

Pokemon Gold/Silver/Crystal:

Pokemon Firered/Leafgreen:

Pokemon Heartgold/SoulSilver (my recomendation):

Everything else is irrelevant. JK, I'm just lazy.

Gen 2 for sure, that's the best one to start and the best overall as well.

I consider Pokémon to be one of the best RPG series ever created. I played Blue back when it was new and I managed to collect all 151 and I must say, the achievement and fun factor while playing a Pokémon game is unrivalled. After playing Pokémon GO, I might go out and buy Sun or Moon on release. There amazing games. I suggest playing the originals Red/Blue/Yellow only because I find the original Pokémon to be much better than the later ones. That’s just my opinion and preference.

Heartgold and Soulsilver would be the best place to start. They are the Gen II remakes, and you can say you kill two birds, if you aren't too interested in the Gen I story. Then the best option would be to jump to Gen IV and Gen V which are the DS games, jumping Gen III because you will play that in ORAS, but if you have a GBA and can found Emerald then go for it. Then pass to XY and ORAS which are the most recent, and of course, afterwards get Sun & Moon. Then if you are interested get the Gen I games in the VC. So pretty much a order like this:

- Heartgold/SoulSilver
- Diamond/Pearl/Platinum
- Black/White
- X/Y ORAS
- Sun/Moon
- If desired Red/Blue/Yellow.

Though just don't begin with Gen VI (XY) or Gen VII(Sun & Moon), since then you may have a hard time accoplating to the older games, since they can be slower in certain things than the newer ones, which makes sense seeing how they are older.

Asking "What is the best game in the series?" isn't possible when you talk about Pokémon. Everyone has a special relationship with the first game they played in the series and will defend it to death. That beeing said I'm just like you the kind of person that thinks the games in a series should be played in order, even though I only started from Emerald. If you have problems with Black/White, then buy Pokémon Yellow (also available on the 3DS Virtual Console) which is basically Red/Blue (the first titles in the series) but with colour and small changes here and there, also the Pokémon currently available in Pokémon GO are only those available in Red/Blue/Yellow

Play Pokemon Leaf Green/Fire Red if you feel that you'll lose interest. But my opinion of the best Pokemon game...I'd go with Pokemon Sapphire/Ruby/Emerald. They're my favorite Pokemon games of all time. If GBA is too old, there's also 3DS remakes. The music is amazing, the story isn't much but what's there is solid. The Pokemon designs still had their dignity (come at me, lol!) and the locales are very memorable.

My Choices:

1.) Ruby/Sapphire Emerald

2.) Red/Blue/Green

3.) Gold/Silver/Crystal

4.) Diamond/Pearl/Platinum

5.) X and Y

6.) Black and White

7.) Black and White 2

I legit thought this was a DS game. Amazing! Definitely gonna check this one out!

Emerald>>>>>>>>>>>>ORAS, Otherwise he would never experience the best Battle Frontier of the series...

Try FireRed since it's a remake of the first gen which also adds some extra stuff. HeartGold is the same, except for gen 2.