Good luck with your licence. I found it a hard test when I did my DAS a few years ago but did pass first time, doing both MOD 1 and 2 back to back.
You say you're not fussed about top speed, but smaller bikes are very buzzy at the top end of their range (as you know on a 125) so don't be afraid to go bigger for motorways and it's nice to have power in reserve. Big bikes ride better there and less twitchy in side winds, but are less agile in the city.
If you want a solid commuter bike, you can't go wrong with Honda cb500 or similar. There's a lot of older ones still chugging away - tatty and less stealable, but ultra reliable and cheap to maintain. 70mpg, more than enough power for the motorway, not too fat to filter.
Some of the older (2000-2010) BMW 1100-1200s are fairly good, either GS or RT. Lovely torquey engine, good presence, comfy and nice on the motorway. A bit fat for filtering sometimes.
Good shout on keeping your 125. They're a hoot and great for bombing around the lanes or cities.