Just saw the word Pokemon and I opened this thread like crazy.
I am 20 years old and I still like Pokemon... A lot. I would suggest starting with the first ones, even if you just do a quick run through them. Go about them in order! That will help with your nostalgia, as it might come close to what we experienced at such small ages; you played a game and waited for the next one to come, etc it's just that this time around you don't need to wait
Every game has a great story, in my opinion. Some people hate the generations after the 3rd one, calling out that the original Pokemon were better etc, etc I call bull feces on that one, they probably didn't even play the newer gens or are the typical person who doesn't like change.
So after all I said: PLAY ALL OF THEM!
Side note: 4th gen and later get a little more complicated since Nintendo focused a little more on to trainers who can get into the technical training (IV's EV's, Nature perks, etc) which I also consider fun but others may find a little complicated. Nevertheless you can still play the games ignoring those things. Note that IV's and EV's exist since the first generation (Blue, Red) but nobody really cared at that time and did not know how they worked.