First of all I would watch the original anime if you haven't. If you like it, then go ahead and watch Cinderella Girls. If you want to skip that part that's fine, but none of the games have English translations or patches. You have a couple of options in terms of what kind of game you could play:
If you're looking for the rhythm games skip the first 2 choices
Idolm@ster 2: This would be my recommendation if you're looking into getting into the console games. The game is for ps3/xbox 360, there's a really good English guide here: http://imas2.wota.info/strategy/beginners-guide
If you're looking to learn Japanese, playing this game could also be helpful because it's fully voice acted, so you can hear the voices along with the text being read. If not, the guide is pretty easy to follow and helps a lot. I really enjoyed this game. It's an idol production game, and only has a small mini-game type thing that can be compared to a rhythm game (Gameplay video here: https://www.youtube.com/watch?v=LpCzdLvobDQ). You get to pick your 3 favorite idols and produce them. There are multiple endings depending on how you produce your idols.
Idolm@ster One For All: Also for the ps3. I don't know much about this one because I haven't played enough of it, but it plays about the same as Idolm@ster 2, the only difference being you get to produce more than 3 idols if you want to. There's not really a very good English guide for this one, so I would get a feel for the game with 2 before playing this
Idolm@ster Platinum Stars: This one is for ps4. Graphics are very good and song selection is very good, but I've never played it myself. This game actually has more of a rhythm game instead of just a "press the same button repeatedly" game. Here's a little bit of gameplay, I couldn't really find a better video so sorry about that: https://www.youtube.com/watch?v=KUYRo3KSQfA

If you prefer Cinderella Girls/ Have no Preference:
Probably the best Idolmaster game is the Cinderella Girls mobile game. I'm not going to necessarily recommend this to you, because mobile games are a dark hell to enter, but here's a video of the gameplay: https://www.youtube.com/watch?v=gPW84z33mfg . This game has a fairly large community, so you can find translations for a lot of the text and videos on youtube or twitter.