When price is comparable, just go for the M135i. It will be a continuous experience of driving a real performance car. The 125i is also fast, but it will not leave such an omnipresent flair of power and torque. The 125i is a very good car, but the M135i is a very special one, even without the leather upholstery or big navigation.
For what the M badge concerns, I guess you have to put it on! Your point is valid... probably all of us partially also buy the car since it makes us look good, professional, sleek and well educated. I'am convinced this is an idea we have, since 90% out there doesn't have a clue about our cars.
I have an M-steering wheel in my 520d because I like the feel of it. And although I have the 520d badge on it and only the 17inch std rims, people ask me whether this is a real M5 I'am driving!