Record of Agarest War is now out! Go buy it!
Download the user manual here.
"Easy" is recommended for first-time players, and those who just want to enjoy the story and character events, without too much of a challenge.
The story is just the same as in the other modes, and as long as you remember to level up your characters, you should be able to proceed through the game smoothly.
"Normal" is more balanced than "Easy" or "Hard", so choose this if you want more of a challenge than "Easy", but don't want to get destroyed by "Hard".
Enemies in "Hard" are much more difficult, and the game is much more of a challenge. This mode is recommended for people who want to get the most out of the battle system.
The resources you amass (Party Points, Experience Points, etc) will carry over into a new playthrough if you start with the New Game + feature, although your items won't carry over. You can start a New Game + on any difficulty.