I went from a 1992 125cc Piaggio Zip scooter to a 2004 125cc Jinlun Texan (cruiser) until I got used to handling a bigger bike (spent a year on scooter and 8 months on the 125 cruiser).
since then i've been through a few bigger bikes, but right now i'm 24 and riding a 1990 Yamaha XV 535 (Virago) that i picked up on ebay for £550.
it's a good little bike, but i wouldn't recommend going from a scooter to it.
If anything, i'd seriously recommend spending some time on a low-powered cruiser or street bike until you're fully comfortable with it, riding a BIG bike (250cc upwards) is a huge step up in power from a 125/150.
If you've got the money to maintain it, the older Jinlun Texans (honda shadow clone iirc) are excellent bikes to learn on. They feel big, look cool, don't have enough power to kill yourself on, are cheap to buy, easy to maintain (they do go wrong, A LOT) and are very difficult to crash compared to other small cruisers (wide foot-boards, you'll scrape the foot-boards/exhaust on the floor long before the tyre grip lets go around corners)
Personal Experience, 5 years motorcycling