YBR 125.
I had one for a couple of years now, cheap to buy, pick up probably an 05 plate for 800 quid. Most of them have fairly low mileage on them as most people just use them to practice on for their test.
4 stroke, reliable, does about 60mph, size wise is probably about right. Doesn't ever really need anything doing, mines done about 9000 miles. apart from a new chain and sprockets, a new back tyre and fork seals it hasn't needed anything else.
It does need another chain now but only as the last one that was put on by the garage was cheap and poor quality.
About £9 to fill it up and that returns around 180 miles, and thats with 15 stone on it driving it flat out wherever possible.