In the beginning, unlimited?

Hello, after 10 years of accident-free driving I will make my mople ticket here in England this summer. Since I am old enough, I can also do the unlimited, before that I already made my CBT (compulsory basic training) for motor bikes up to 125 ccm; with which I can drive for two years. I would like to drive already a 650ccm to Scotland and Italy, but I have quite great respect (certainly not afraid!) for the power/weight relation and ask myself whether it makes sense to have such a jock. A friend of mine also made the “Direct Access” and is therefore gurgled throughout Europe, but there is still the middle way from A2 to 34 HP. My question: I am now between 125ers, A2 and unobstructed FS back and forth, of course also the costs play a bit, but more the safety. What do you suggest to me? I definitely want to travel, still the moppel must come well through the London city traffic n. I doubt you can travel stress-free with a 125er, but if I do the A2, can I do all this on a 34hp machine, gain experience and have my fun? Thanks for your answers, DJ