Famitsu.com managed to get some new screens of Persona 4 Arena's home conversion. Included in the handful of shots is the game's mode select screen:

The screen shows the following options:

• Lesson Mode
• Story Mode
• Arcade mode
• Score Attack Mode
• Training Mode
• Challenge Mode
• Versus Mode
• Network Mode
• Contents Market
• Replay Theater
• Gallery Mode
• Option

The site does not have details on the modes, but you can probably figure out what most of them are based off the name.

The other screens show scenes from the story mode. When you start off the game, you'll have access to four characters: the main character, Chie, Yosuke and Yukiko. Other characters will be unlocked as you play. The main character's story begins with a reunion with his friends and family.