I'm only a couple of inches taller than you, and weigh the same, and I bike.
I'll second DebW on the wheels with higher spoke counts being one of the most important things regarding strength on any bike you get. I've been suffering the frustration of low spoke count wheels, and it's annoying. (I've recently remedied that by ordering a set of handbuilt wheels with a higher spoke count.)
Just start hitting shops and trying out bikes. Lots of bikes. As many bikes as you can get your butt on--steel, aluminum, whatever. You won't know what you'll find most comfortable (and fun...never forget FUN) until you ride some.
When I was shopping for a bike early last year, I went in thinking I needed a WSD (Women's Specific Design...and was particularly coveting a Terry), but it turns out those were the most inappropriate/uncomfortable frames for me. Then I thought maybe I wanted a steel touring bike, and they were definitely super comfortable to ride, but something was still not quite right--they weren't saying, "Hey, lady, I'm your bike." So, I kept trying bikes. I ended up with an aluminum frame road bike, because of everything I tried, it was the most comfortable (as far as frame size/geometry) and the most FUN to ride--responsive, light...and pretty.
But, if the bike you love doesn't come with the kind of wheels you need, try to work with the shop to get something more appropriate.
Good luck!