Lots of good advice in this thread. I've been riding for over 30 years (and commute every day on a motorcycle), so I'll just go ahead and impose my advice too
What you need depends on how / where you're gonna ride. I ride my girlfriend's '08 Ninja 250 for shyts and giggles every now and then, and it's fine for city riding, or tighter twisty roads. It's 1000cc smaller than my Bandit 1250S, so if I think it's good fun, you'd probably be ok. Wringing the snot out of a Ninja 250 on an on-ramp is more fun than blasting a Hayabusa down a straight line.
The CBR 125 is a flyweight, it's ok for commuting, but not a lot else. Though people who compare it to what is ridden in 3rd world countries don't have a clue... I was riding step-through motorbikes in Vietnam last week, and they are not at all the same thing as the CBR. The CBR is a real motorcycle, but not much power. Like I said, good enough for commuting though, but forget the highway.
A modern 600cc sportbike is too much bike to learn on. The 500 Ninja / 600 Bandit / EL6 type bikes are much tamer, and are a good option. Even the SV650 is fairly strong, but still much more manageable than a 600 pseudo-racer.
Take a course. You're a ###### if you don't. Yeah, it's actually that simple. Ditto for proper protective gear... helmet, jacket, boots, gloves at minimum. If you aren't down with that, hey, that's what they call natural selection.