This is a very helpful website for newcomers looking to purchase a bicycle:
http://www.bikesrnottoys.com/Given your expressed riding preferences, you may want a hybrid. I believe good, but not flashy, hybrids can be had for $300-$400, perhaps even less, but don't quote me on that.
As far as accessories go: I think a rack over the rear wheel is extremely helpful to help ferry things around like books and small amounts of groceries. A saddle bag (small bag that fits under the seat) is also extremely helpful, to carry emergency supplies (spare inner tube etc). A water bottle holder mounted on the bike frame is very helpful for longer rides. And if you end up with a bike with a small frame, you may need to also purchase a special bottle that will fit. (For larger frame bikes, grocery-store-bought plastic water bottles fit.)
A good hand pump that can be mounted on the bike or fit in the saddle bag is of course crucial for when you get flat tires. A foot pump is much easier to use, though, and is good to have for the weekly tire pumping event. I didn't get one for years, but now that I have one I wonder why I waited so long.
That's pretty much all I can think of that I would consider essential or extremely helpful. Other things you can purchase as you feel the need for them.
(Oh, if you plan to do any riding around twilight or after dark, get a headlight and one of those strobe light contraptions to make sure you aren't completely invisible to drivers!)
EDIT: I should add that bike stores sell special saddles made for women. My wife got a $60 one at the time she bought her new bike a couple years ago and swears by it. Makes riding so much more comfortable, she says. (I'll take her word for it, though I've always just stuck with the saddles that come with the bikes.)
EDIT: Ok, I thought of something else. If you don't wear glasses normally, consider puchasing a pair of bicycle glasses with interchangeable lenses (clear and dark-lenses). Otherwise, bugs could fly in your eye while you're riding and that's no fun. Again, my wife swears by her bike glasses. (They aren't cheap, alas.) I don't have them, since I wear glasses normally.
--Peter