There is no perfect advice possible if you arn't a totally novice, as you have a lot of experience in bike riding already.
So you have to find it out by the hard way, asking friends or clubmembers if they will share their bike with you for practising. The 125cc are good but needs active throttle, the 250cc are good too needs less attention to throttle, the 280 - 300 again need again attention not to use too much throttle and can be ridden lazy too. Certainly the 250cc is enough for nearly any beginner, the 125cc can rasp on your personal image, as it's too the schoolboy machine. The surplus of the 125cc of less weight I believe is not important for a beginner, some 125cc are very good as the Scorpa that's fittet with much flyweight, some are more nasty as the Beta which has less flywheelweight and is therefore more peaky.
But much more important is that it will suit you ergonomical, the power question is one point the way you feel comfortable on the bike or not much more important in my view. As you search for a used machine too I would therefor suggest you try to get the best used serviced and maintainced bike possible and don't look so much at the cc displacement. If you have found a bike ask an experienced rider that doesn't have branded glasses on about his opinion and in any case do a test ride.