Assuming you want a mountain bike, these are generally designed for more rugged terrain and aren’t necessarily for cruising at high speeds on flat streets. Even within the category of mountain bikes there are a variety of specific bikes designed for several different riding styles and terrain. You will need to figure out what type of riding you will be doing most of the time. Is it smooth trail riding, cross-country racing, all mountain cruising or lift accessed gravity mayhem? Make sure the bikes you look at fit your riding style and not the sales staff’s.
Cross country mountain bikes
These usually have less than about 4.5 inches of suspension travel. These bikes are built for efficiency, low weight, and self-propelled speed. While they can handle most trails, they do not handle the rough stuff as well as longer travel bikes. So, if you want to win a cross country race, get to the top of the hill first, or if you ride on relatively smooth trails then these bikes are for you.
Mountain and/or Trail Bikes
These usually have about 4 to 6 inches of suspension travel. These bikes are built for more aggressive terrain than cross country bikes but are generally slightly heavier. They aren't exactly cross-country race bikes, but they are perfect for aggressive trail riding as well as long epic rides. If you are looking for an all-around mountain bike that can take you almost anywhere without busting a lung, these bikes are for you.
These usually have about 6 to 8 inches or more of suspension travel. These bikes are built for abuse. Big drops, jumps, long shuttle rides, and other stunts are where these bikes shine. While most of them are still designed to get you up the hill as well, you will notice the extra weight. If you want to spend most of your time in rough terrain, big drops, jumps, and manmade stunts, and you don't care how long it takes to get you there, these bikes are for you. These are also great bikes for riding the lifts at your local mountain bike park.
These usually have about 7 to 10 inches of travel. These bikes will suck up almost anything you throw at them, but pedaling up a hill can be quite a challenge. Downhill bikes are designed for high speed and highly technical downhill racing and little else. If you think you might want to get into downhill racing, get a freeride bike. If you're really serious about it, a dedicated downhill bike is for you.
Within all of these bikes there are often styles that are specifically designed for the female physiology. Women's specific mountain bikes are designed to fit a majority of women but cannot be designed to fit all women. You should try to test ride both women's specific mountain bikes as well as non-women specific bikes and decide for yourself which designs fit your body best. The majority of women-specific designs are designed around an average women's body. This body standard is smaller, lighter weight, and has a shorter torso and arms than the body standard of the average male that most non-women specific bikes are designed around.
If this average female body standard describes you, then you will most likely find a better a fit with a woman's specific design. Otherwise, if your build differs from this average women's body standard, a non-women's specific design may be a better choice. For some women it simply boils down to size. There are a few companies now that offer extra small and XX small size frames; some are women's specific while others are not. Generally, you won’t notice a big difference unless you’re a very petite woman but if you can’t find the bike you’re looking for don’t be embarrassed to look in the kids’ sections; kid’s mountain bikes are every bit as professional as adult’s bikes they’re just designed smaller.
Comfort vs. Efficiency
The next thing you want to determine is if you need a full suspension or a hardtail bike. A full suspension bike has suspension on both ends (sort of like shocks) and a hardtail has none on the back. I always recommend a full suspension mountain bike if you can afford it. Hardtails, without rear suspension, are lighter weight and pedal more efficiently but full suspension designs offer more comfort and better control. You will want to decide based on your price range, riding style and terrain.
Full-suspension mountain bikes are much more comfortable, enjoyable, and better controlled when compared to their hardtail counterparts. The tradeoffs of a little extra weight and slightly less efficiency are well worth the added benefits.
Some people will disagree with me on this subject. Hardtails do pedal more efficiently especially when the terrain is smooth. Hardtail mountain bikes are also a bit lighter than full suspension designs and require less maintenance.
A good number of cross-country racers still use hardtails for the above reasons, but most endurance and other types of racers have switched over to full suspension. I should also note that hardtails are also especially popular among the dirt jumping crowd where they pump better from jump to jump.
Unfortunately, full suspension mountain bikes are a bit more expensive than hardtails. If you can't afford a full suspension with decent and reliable components, I would recommend buying a good reliable hardtail from a specialty bike shop before going to a mass merchant such as Costco or Wal-Mart for a bike that may fall apart after you ride it for a few days.