The story in Dragon Quest games is usually pretty solid. Not as "up itself" (sorry) as some of the Final Fantasies (you could sum up the plot in a couple of paras), but pleasant in a "fairy tale" kind of way.
Over the games, they've tried a few different styles of storytelling, but nothing too unconventional (in one game, you played each hero individually for a few hours, before switching to the next until they all united near the end). It isn't afraid to try a few variations (eg. shopkeeper as a character class, or shepherd) but largely sticks to the formula.
Battles are turn-based, and the story exists to move you forward from town to town. The characters are pre-set, and typically join at intervals throught the game. They usually have charm/personality.
Each area will typically have some sort of main "side" quest to do to sort things out in that area, and once that's set to right, you can move on to the next area.
In previous games, there have been interesting innovations and/or mini games. For example, one region/town required the use of the character's pet (mouse? miniature space hamster?) to explore and enter areas etc. There may be monster collecting / battling or other mini-games too.
Dungeons usually have a strong theme, and may well include puzzles.
Character levelling and skill aquisition is usually pretty solid, and there's often a substational "post game" too.
All in all, if you can cope with the very anime look/style (creature designs by the guy who created the characters for Dragonball Z), Dragon Quest games generally offer a really good "meat and potatoes" JRPG experience, with an attention to detail and love / charm that makes it special.
It is definitely NOT a final fantasy game - it doesn't feel the need to constantly throw out everything its predecessors got right - and some people may find the storyline lacking all the political shinnanegans or myriad of personal details/sidestories that you get in (say) Witcher or Baldurs Gate.
But for those who take the journey, you tend to get a beautiful balance of old school and modern in one tidy package. You'll get the warm-and-fuzzies that you get when replaying older games, but with the fresh look of something more recent.
Of course, that's no guarantee that this version will be good, but it has been out in Japan for a while to high acclaim, and the western version gains full voice acting, extra content and a visual polish, if memory serves. Looking forward to my birthday!