Xbox 360 games are usually region locked. So, you will need a JP Xbox 360 to play JP games. JP and Asian games usually won't work on a US Xbox 360.
About 99% of PS3 games are region free. So, if you have bought the PS3 version of Idolm@ster 2, then you could play it on your US PS3 with no problem.
The PS3 version of Idolm@ster 2 is the better version since it has more content than the Xbox 360 version.
I would say try to buy a PS3 because that's the only way to play Idolm@ster 2 and One for All. Plus, the PS3 has a lot of good games, so it's a good investment. Remember, nearly all PS3 games are region free so you can play JP, Asian, Europe, and US games on a US PS3.
I would say return the game if you can and get the PS3 version of Idolm@ster 2. Also, if you can pick up the newest game which is One for All.
Just letting you know that the main games take a lot of time and patience, so they aren't so easy. There's somewhat of a learning curve. So, it's going to require a large amount of commintment.
Plus, they have a lot of DLC content which cost a lot of money. For example, in One for All you'll be spending much more money than the game itself just to complete the characters EX episodes story. So, be prepared to spend a lot more money than any game you ever bought.
Of course, knowing Japanese helps a lot. Obviously, you don't need to learn Japanese to enjoy the games. I don't know Japanese, but I still played through them by using the online guides.
Here's the guide for Idolm@ster 2http://imas2.wota.info/home
This is a supplemental guide for Idolm@ster 2 in case you need it.http://imas.wikia.com/wiki/The_Idolm@ster_Gameplay_Wiki
And, here the guide for One for All if you decide to get ithttp://idolmasterofa.wikia.com/wiki/IDOLM@STER_One_For_All_Wiki