I started with a 2006 honda cbr 125r.I decided to splash out on it to get more riding time behind me while i was waiting to do the direct access.I was happy i got it,hassle free and i knew i wouldnt lose much money on it.I lost 300 quid which i could have easily lost if i bought a piece of junk,plus it was great on fuel with fairy good handling.
The thing is,it was a 33 mile commute on a fairly fast road with a climb of around 1000ft so the ascents were a struggle (13+ stone!)to the point where you would consider it dangerous.You need to get up to speed quickly to be safe and with a 125 in (what you say) busy traffic,i would get something as powerful as possible within the regs.Maybe a restricted 500/600cc would be a bit more grunty but i would consider the traffic level on your trip and think twice about the bike you plan to go for.
Varaderos look like a nice riding position.Would be a nice bike to learn U turns on! Not sure how much slower these would be over a cbr 125 though.
As good as a bike the suzuki bandit may be,the size and weight of one when i first put my leg over it scared me.The thought of owning and learning on one would put me off motorcycling. The cbr had a lot less power but it wasnt a handful.