Have you ever ridden an RS125? 2 stroke heaven! probably the closest to a real GP bike you can buy, made my R1 feel like a bus through the twisties.
Yup I have.
I wouldn't want to commute on one though and as quite a number of my mates proved when we were younger, italian 2 strokes are less than reliable as a package - especially when used in the wet.
Don't believe for a second you'll go faster on a 600. Those little race rep things beg to be revved and need to be to get anywhere. You'll be full throttle EVERYWHERE!
My personal preference would be something with a wee bit of torque so you can relax and cruise and nip away from traffic lights etc when required.
If you are set on a 125 then I'd get a scooter. Makes more sense for commuting in my eyes, can stick your helmet and bits and bobs under the seat and they are nippy round town.