Go to a few good bike shops. Play dumb and see what they sugest. Remember what size they put you on so you can compair the sizes all the shops put you on.
Something you need to decide on befor you go to the shops is, what type of riding do you want to do. This can help you/them choose the type of bike best for you.
True, they do make bikes built for women. The old days a girls bike was a step thru style frame. They still have "step thru style frames" but they are not just for girls. A woman specific frame is built for a womans body proportions. At a quick glance you would not be able to tell a mans bike from a womans.
Road: fast, light, small tires, great on road, not great on gravel.
Mountain: heavier, fat tires, great off road and gravel roads, slower on road.
Hybrid: a mix of both road and mountain. (nice all around bike)
Triathalon: tight, fast, not great for long rides.
Fixed gear: single speed, no brakes, pedals always spin (road or Mtn)
Trials: kinda like a mtn but for hopping around on obstacals (sometimes, no seat)
Cyclocross: kind of a road bike built for mild off roading, 700cx35 tires (road dia but fatter)
Cruiser: the old style, more upright sitting, some single speed some 3-5 gears, seen on beach type boardwalks.
Here is a guide to read reviews on a lot of bikes.
Once you decide on a type of bike, ride a bunch that are built out of the same materials. Just because there are 10 bikes all built out of one material doesn't meen that they will ride the same.
I rode about 12 full carbon bikes whan I bought mine. some in my price range and some 2 to 3 times more. I'm light and bikes are made for the average to heavier person. Most were too stiff. They will have different geometry and some feel lazy while are twitchy