>>43234873Diamond/Pearl were pretty bad, really needed the third version Platinum to fix it up. I personally am not a huge fan of these games, but the lore they had was really cool. Look up the Canalave Library stuff, and read the stories.
HeartGold/SoulSilver are commonly regarded as contenders for best games, if not the Gen 5 games. Quality remakes that stayed mostly faithful to the originals, and improved with probably the best touchscreen interface and gimmicks like walking with any Pokemon.
BW was aimed at an older audience, actually has an attempt at a plot, and probably has the most memorable characters. BW2 was their big spin, making a sequel story instead of just an enhanced third version. BW2 is content-packed too, most notable is the Pokemon World Tournament, which lets you fight practically every Gym Leader and Champion from the previous games, and even had download events where you could fight the teams of real life VGC finalists too.
Let's just say that the DS era was considered the peak of the franchise by most, while the 3DS was the start of the downfall in terms of barren campaigns and content. Literally the only thing that carried XY back in the day was the online community. So if you liked X, then you should definitely check out 4/5.