Cool that makes a lot of sense.
If your on a budget for the bike then anything remotely sexy is pretty much out as sex costs 🙂
The amount of fun you can have on a 125 will depend on which one you get. All have crap power but some have nice handling and are fun to ride (if not a little frustrating)
One of the changes in the second hand bike market is that smaller lower power bikes now have a market again as people who didn’t do DAS or are not 21 or over are limited to 33BHP so bikes that typically fell in between a proper big bike and a learner bike now have a market again.
If you want to run something older and interesting though its going to cost you in the wallet or in time spannering yourself.
So it might just be worth getting something not so cool to start with enjoy it build up some no claims and then if you enjoy it move up.
Just try not to be put off, the difference between a crap bike and a good one is huge.