So as much as i love the phantasy star games, i should probably preface a few things about the first 3 games.
The first 2 are archaic as hell, not bad, but archaic, what i mean by this is that you have to remember both came out in the mid to late 1980's, with all the drawbacks games of that era had, maze like maps with no guided path, very simple combat systems, and far higher difficulty than modern day games on average, that being said i consider 2 to have one of the best stories in any game series bar none, proof that you don't need 30 minute cutscenes to tell a compelling story and that sometimes saying less can be a better storytelling method than 30 minute cutscenes.
Oh and phantasy star 1 plays differently than 2-4, 1 is more like shining in the darkness in that it's mostly a first person dungeon crawler except on the overworld.
Phantasy star 3 is the black sheep of the series, i wouldn't call it a bad game, just experimental, it's story and gameplay flow is handled vastly different than 1, 2 or 4's, if it wasn't named phantasy star it would probably be treated far better.
4 is...a masterpiece, for 25 years it was my favorite game of all time, only unseated by ys 8 lacrimosa of dana a few years ago, 4 holds up extremely well even 30 years after it's release.
All of the games are chronologically linked, with exception of 3, kinda (3 takes place at the same time as 4, but both games have little to do with each other, 2 takes place 1000 years after 1, 3 and 4 take place 1000 years after 2, 3 could be considered something like a parallel universe game).