Suzuki GS125's are good. solid little engine and return 100+ mpg.
Extremely cheap to run, maintain, simple, forgiving, nothing to damage when dropped (just glue turing lights plastics). Neutral riding position. Perfect IMO. From there you can go more racy, or enduro, or chopper, whatever you fancy.
Cheap to buy, won't loose much on resale.
And yes, I'd definitely recommend 250cc afterwards, before anything bigger.
For learning, first bike - get an old one, for 500-800 euros max, ride, fall down, learn, sell it on after a year.