Man where is Sarge when you need him, he is the resident DQ overlord.
Maybe... I'm the
Dragonlord?
Dragon Warrior for the NES is probably the worst place to start. I know it's the first... but that's the problem. There's not much to it, it's incredibly grind-heavy, and while it's amazing for what it did in the day, it has been surpassed by nearly everything on the system. If you
have to play a version, take either the GBC or SNES versions. (All that being said, I still have a soft spot for the game, it
was my first RPG. But I'm not blind to its flaws.)
The series shows marked improvement in the second game. Much larger world, more enemies, three party members, more spells, and so on. You still may want to try the GBC / SNES version for that, I think they've adjusted the difficulty curve a bit. I don't think the game was nearly as grind-heavy, either. I'd say the original
Final Fantasy is probably a touch better than
DW2, but not by a lot.
DW3 is where the series really shines. I love that game. It's important to play the first, in retrospect, because it gives much more heft to the story, such as it is. You've also got many more strategic options, as you can build your own party, and there are eight classes in total (Hero, Soldier, Fighter, Merchant, Pilgrim, Wizard, Sage, and Goof-Off). It's just a great, great game, in any form. I've played through the NES and GBC versions (which add new classes on top of those mentioned, and new weapons and personality stuff as well), but the SNES version is
pretty. You'd probably want to roll that way.
Dragon Warrior IV is also great, but at this point, it's another game that's a bit better on the DS, simply for pacing concerns. Not that
DWIV is bad, of course. It's great, just the DS version helps with some folks that might not appreciate the slower pace of the NES version.
This advice holds pretty much true for
Dragon Warrior V as well. There are multiple ways to play it. I wasn't particularly smitten by the SNES version, but the DS one was aces. There's also a PS2 version that has been translated. If I ever get the itch to play the game again, it'll probably be through that. Everything's polygonal, though, which makes me miss the phenomenal spritework in battle.
You've got two options for
DQVI, SNES and DS. I really enjoyed both, and they exhibit the least amount of differences. I'd probably roll with the DS version, though, seeing as how the translation for that is completely finished.
Dragon Warrior VII is long. Really long. There's a 3DS remake now, hopefully we'll get it. I loved the game, but it's one of the slowest in level pacing, if not actual plot pacing. That gets moving pretty fast beyond the opening sequence.
Dragon Quest VIII is PS2-only, and it's a really, really pretty game. Great fun. There's some reduction of strategic depth, ditching the class systems in
V-VII. But the localization is superb, and we even get rockin' British voice acting and a actual symphonic soundtrack.
Dragon Quest IX is... well, it's fun, but it's also very different. You can play traditionally, but there's also a push towards mini-quests along the way, and an almost MMO-lite feel to it. It's a bit of a bridge between the previous games and the MMO they just released (curse their sorry hides!). Fun stuff, but not as good as the DS remakes, in my opinion.
...wall of text. Yeesh. You'd think I liked
Dragon Quest or something.
EDIT: I should say which I think is the best, shouldn't I? That's... actually not easy. I think for the most emotionally poignant tale, you have to roll with
DQV. For gameplay, I think
DQVI ends up being one of my favorites. For interesting characters,
DQIV is great.
DQIII is great for delving into the backstory of the original trilogy.
DQII is good if you want a challenge, at least in the NES version. For sheer mass of content,
DQVII is tops, and for sheer spectacle,
DQVIII is the one to roll with. It's definitely the most modern. And finally, if you
like some of the MMO-ish mechanics (and more puns than you can shake a stick at),
Dragon Quest IX is the best.
That leaves out the original, but it's still important from a historical standpoint. Play the faster versions, and it becomes an enjoyable snack of a RPG.