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I guess you're thinking about the motorway part of the journey and keeping up with cars. You can't ride on a motorway with L plates anyway (which you'll need if you only have a CBT). Try taking an alternative A road it would be more fun anyway.
T junction safety is one of the big problem areas of motorbikes and where you need to worry most, getting overtaken by cars in almost any scenario doesn't pose a huge risk as you're not that big an obstacle. It doesn't happen very often anyway.
Maybe try a 5 day course where you go from no license to fully licensed.
I’m fine with an old/cheap/hard to damage bike and I don’t want to hurt myself (or anyone else) but I also don’t want to waste money on a bike which isn’t going to work for the riding I want to do. Had no idea until recently that a 125 tops out at ~65, which doesn’t sound great for keeping up with cars.
My only bike experience (other than cycling obvs) is riding a 125 scooter (with broken speedo) in Thailand 🙄