I've never heard of Junei Fe before so I can't comment on that, which also means I haven't heard it as being one of the good pills for acne. But then again, the pill is so dependent on the person so it could work for you. Alesse broke me out terribly but my roommate's who also has acne has been on it for years so, who knows.
I'm pretty sure there's almost always initial breakouts with the pill because your body is adjusting to the synthetic hormones you're putting in your system. I'm on Diane and I had my initial break out probably near the end of the first month. They say you should give 3 months for any acne treatment before you start looking for results, but with the pill it could take up to 6 months. If you have mild - fairly moderate acne though, I would say it probably won't take as long.
As for oiliness, I'm not sure. It might? Diane certainly made my skin less oily, but that's probably because the ingredients are low-androgenic. Maybe you could poke around the hormonal acne threads for more info?