Go for it. Don't let other people (even if they're your family) tell you what to do. Depending on your age though you might want to wait till you leave home and such.
I'm female, 5'4, 140lbs, and have been riding bikes for 4ish years now. You have to know your limits and what suits you. You also have to know your riding ability. Most crashes are caused by inexperienced riders and/or other cars not looking for them. The only way to get experience is to log hours though, so I have nothing against beginners riding, BUT the main thing is other drivers. They simply don't look for motorcycles no matter how brightly colored they are. Going on the road with other drivers you're taking a risk even if you are the best motorcyclist out there. Also, riding a bike you are more likely to get fatally hurt; let's face it 5-10 tons vs a small bike and flesh. Also, small accidents, slips bumps, and bruises do occur, but can be avoided by taking the right precautions.
Okay now that I have the warnings out of the way... bike for you.... I've been checking out new bikes and the Ducati isn't bad since they sit relatively low and don't force you to bend over the tank like most street bikes. Harley and other cruiser bikes sit nicely as well but they weigh and cost a hell of a lot more. You want to be able to lift the bike up if it ever falls. Trust me Ive had experience with over sized bikes they are not fun and can be extremely dangerous. The Hondas they're making now sit fairly low too, but some of them do force you to lean over the tank. Another good beginner brand/type would be the ninjas and Yamaha.
I wouldn't go over 600 though. If you have never ridden a bike before or took a class for it id suggest a 250. If you have some experience you want a 600 because you'll outgrow a 250 fast and you don't have need for anything around 1000.
Don't rule out dual bikes. Duals are, if you didn't know, a street legal dirt bike. They don't force you to lean over the tank and I find I have better balance on those than a large clunky street bike. Plus if you get the urge you can go off road lol. The only drawback is they tend to run on the taller side.
Since you didn't state it I'm guessing you have no prior experience on bikes or have any bike classes under your belt. TAKE ONE! They not only teach you a lot, but they lower your insurance, AND they can waive the motorcycle tests saving you time at the DMV.
Last words: Take a class, take it slow, know your limits, wear the correct protective gear at ALL times, watch out for other drivers, and be yourself. You may only have one lifetime to do everything in, but as far as we know you only have ONE life to live, don't waste it on acts of stupidity.