Scooters come in 50cc, 125/150cc and >250cc engine sizes, and 10, 12 or 14 (even 16) inch wheel sizes. Basically, your gamut runs from limited speed mopeds to small motorcycles with step-through frames. Many new scooters have CVT (twist-and-go) transmissions, while older ones (or retro ones like the Stella) have manual transmissions with a clutch lever (though instead of toe-shifting as on a standard motorcycle, you wrist-shift with the left hand). Older ones are also going to have two-stroke engines rather than four-stroke, which in practical terms means you will have to add oil with your fuel for the engine to work (and the exhaust will have a distinctive oily smell to it as well).
Since you mention being broke, I assume you’re looking for small and cheap, which means relatively low powered. Plenty of people ride around town (by which I mean Manhattan in NYC) on 50cc scooters, but myself, I’d prefer a 125cc as on a 50cc scoot, you’re topped out at around 40 MPH unladen. If you’re planning on carrying stuff you’d better get at least 100cc.
Which means you’ll likely need to get a motorcycle license. Please don’t equate smaller frame/wheels and engine with “less dangerous” than a motorcycle. True, you won’t be getting into a high speed, 80 MPH collision with the highway divider. But most motorcycle accidents happen in local traffic at speeds under 40 MPH (due to hitting a pothole or curb, wiping out on sand or a grease/oil slick in the road, swerving for a jaywalking pedestrian or car cutting you off, or worst of all, getting hit by a car whose driver “didn’t see” you when making a left turn). Hitting the pavement (or the hood of a car) at 30 MPH will hurt just as much coming off of a Vespa as a Harley if you’re not wearing gloves, a proper helmet (preferably full-faced, if you like your face) at a minimum.
My strong suggestion would be to find, enroll and pass the MSF (Motorcycle Safety Foundation) Basic Rider Course. In most states this will give you a waiver for your state’s road test, as the last day of the course includes a riding skills test. This course will teach you to ride (starting from zero) and also teach you the basic elements of street riding awareness and safety. It’s a good way to combine three important things for a new rider: (a) learning riding skills, (b) learning about safety, and (c) getting your license endorsement.
After that, you can decide on whether you want to get a small motorcycle or a scooter. I ride a maxi-scooter myself to work nearly every day (a Piaggio BV500), and for several years rode a Vespa GT200, but these are not cheap rides.
Some people buy a 50cc scooter (like a Vespa LX50 or a Vino Classic) and then modify the engine with aftermarket kits to increase the engine size/power to 70cc or so. I have no experience with this, however, so I can’t speak to how much they cost or what effect they have relative to simply buying a larger engined scooter in the first place.
Here’s a list of popular scooters by manufacturer, their sizes and price ranges. The dealers listed are all in the NYC area, but you could look up where they’re sold anywhere local to you, or on Craigslist. I strongly advise you to NOT buy a self-assembly scooter over the Internet. A reliable, >100cc scooter will run about $2500 new, or around $2000 used if you can find them (they’re getting quite popular now due to gas costs, and summer is always a hot market for motorbikes of any stripe). Looking for that $800 scooter shipped to you in pieces sent from Asia that gets put together by a lawnmower shop is really asking for trouble in the medium term.
I’d suggest you check eBay, Craiglist and other usual spots for used scooters. If you’re a new rider chances are very, very good that you will drop your first bike within the first 6 months, most likely in a low speed/parking lot incident.
Based on your comment about style, I might recommend a Yamaha Vino 125 (if you’re not too tall). This is a very cute and retro looking scooter that is yet thoroughly modern in technology. You can even get a fold-down rear rack to which you can bungee a box or milk crate for schlepping stuff bigger than what you can carry in a backpack.
As for security – let’s face it, most scooters are small, light and can easily be moved around by hand by two people, or even just one determined and strong guy with a little bit of leverage and a large dolly. The best place to keep a scooter at night is in a garage. If you can’t do that, lock it to something with a chain that goes through the front wheel, put a cover on the scooter (to discourage molestation and random people who like to sit on it and go “vroom vroom” or worse), and hope for the best.