As a Fire Emblem game, New Mystery is in the top two for actual strategy and map design in the series. So starting off, you will be met with the difficulty selection. The difficulties in New Mystery are my personal favorite in the series. This is really the only Fire Emblem game where you can play all the difficulties in order and have an increasingly difficult time. Starting off with Normal, the enemies are similar in strength to the original Fire Emblem Mystery of the Emblem. Because of the overall increased growth rates of the cast and the slightly simpler machanics it makes for an easier experience. Hard mode increases enemy stats by quite a bit, however most of the enemy stat improvements over the higher difficulties are in strength, skill and speed. This means that aside from doubling threshholds enemy durability is kept similar to in normal mode, even when playing on Lunatic. Hard mode also adds ambush spawn reinforcements. This isn't necessarily a good thing to be quite honest. But FE12 does handle these reinforcements better than the other Fire Emblems that feature them. The player is taught to be weary of forts early on and the trial and error nature of the game, in addition to the in-map save points, returning from Fire Emblem Shadow Dragon, make them less of a nuisence in a regular playthrough. As for the third difficulty, Maniac mode, enemy stats are increased again by about the same amount. Maniac mode generally serves a more leniant version of Lunatic, the speed benchmarks are lowered by about two accross the board. Maniac and Hard serve as decent difficulty for no-reset runs which are generally the most fun way to play Fire Emblem in my personal opinion. As for Lunatic and Lunatic Reverse, they are considered to be the hardest challenges offered in the entire series, with high enemy offences, no warp or silence staves (silence is also removed in Maniac), while still being hard in a fun well designed way and is only rivaled by Fire Emblem Fates Conquest in this department. The unit balance however could use a little improvement in the higher difficulties. As some of the later characters in the game, who are meant to serve as replacement characters for any deaths one might have suffered, are nearly unusable. The get onerounded by nearly every enemy. This should be easily fixable with some hard mode bonusses to at least give them enough of a speedboost to not get doubled.
I overall think this game is just a very good experience for any fan of the series, with some of the most fast-paced and fun gameplay.