The Phantasy Star games are all quite different.
Part 1 is a difficult "old-school" 8-bit title with exploration over several planets, lotsa grinding, and somewhat disorienting first-person dungeons.
Part 2 is also quite difficult. It's an early 16-bit game but still feels simplistic and "8-bit" in design. Lotsa grinding still, and even more difficult dungeons (though they are top-down now). I really like the characters and OST in this one, though it's my least favorite of the original four.
Part 3 is the only one with the generational theme. It was designed by a different team and feels completely separate from the rest. It's also "easier" and more straightforward than its two predecessors. Gets a lot of hate, but I enjoy it.
Part 4 is amazing. It sounds a bit snarky to say this, but it feels like a SNES RPG. In other words, many would put it on par with Chrono Trigger, FFVI, etc. Play it.
Some old spin-offs: Phantasy Star II Text Adventures (exactly what it sounds like), Phantasy Star Gaiden (spin-off of part 1), Phantasy Star Adventure (first-person adventure game). Recommended for completionists only. All have fan translations.
The series completely shifted with Phantasy Star Online. Now the games are mission-based action-RPGs (with the exception of Episode III, which uses a neat card-based system) with optional multiplayer.
Overall, Phantasy Star IV and Phantasy Star Online (the original, on Dreamcast) are my faves by a landslide. But I adore the whole series. I mean, c'mon, we're talking retro JRPGs here.
By the way, if you really wanna nerd out you may enjoy this website. Spoilers ahead, so perhaps wait until you're done with PSIII?
http://ps3.huguesjohnson.com/