i run around on a 50cc honda metropolitan, pretty much bulletproof, 100 mpg and 40mph top speed.
i recommend at least a 125cc though if your need more speed (55-60mph) yamaha vino 125, vespa lx, or genuine buddy 125 are my favorites.
the 250s will go anywhere you need them too but cost more.
i would rather buy a "big name" scoot though rather than a no-name or knock off (and schwinns scooters are rebadged knock offs IMO)
there are cheaper and equally as fun, but more likely to have "special needs" whether its mechanical reliability or poor assembly, the wait for a part cpuld keep you scootless all season long.
brands i like = hondas, yamahas, genuine scooter co., vespa (you will pay more just for the name too), kymco, aprilla, italjet, and i have heard some good stuff about TGB and Bajaj scooters but havent seen for myself.