If you are planning on buying a bike to ride 20 miles a day, you definitely do not want to use a mountain bike.
The issues with mountain bikes lie more in the knobby tires as opposed to the weight -- If you're going to be riding on pavement, you want to have as little rolling resistance as possible. However, the lower the rolling resistance, the higher the likelihood of a flat. Fat, knobby tires are only good for keeping yourself upright when you're biking quickly through mud, sand, dirt, etc...
I would suggest purchasing something with City/Touring tires on it (unless you are going for a speed record) -- This will provide you with a good balance of low rolling resistance and durability. Do not underestimate the value of good tires on a commuter bike - this could make or break your experience.
If you are dealing with hills, you are going to want to have gears. I would advise something with an "click shift" mechanism that has easy to read gauges - If you are just starting out, the lever gear shifts can be a nightmare to figure out. Learning to properly utilize the gears will go a long way toward helping you power through steep hills. The theory basically works the same way cars do: low gears for getting up hills or gaining speed, high for flat roads or increasing top speed. One other pro tip - NEVER have all your weight on the pedals while shifting gears - shift your weight to the saddle until the gears have shifted. You do not want to have to deal with a broken or derailed chain while climbing a 40% grade.
I would also think about disc breaks if you are dealing with hills - They tend to brake far more evenly and compensate better for an over zealous breaking hand. This is really not a huge deal, but it is nice to have if you have to brake suddenly on a downhill road.
A couple tips for fit - If you are purchasing a standard bike -- top bar should sit around an inch below your inseam when your feet are flat on the floor. Some "women's" bikes will have a dip in the top bar (this is a holdout from the 1900's, when women would ride in dresses) - Obviously, that's not necessary if you're getting one of those bikes.
If you are planning on riding on hills - Get something with pedal clips/straps - That way, your legs are evenly powering the tires through the entirety of your stroke (as opposed to only providing power on the down-stroke)
Finally, get a comfortable helmet. This is another HUGE problem for a lot of beginner cyclists. Make sure you do NOT skimp on a good (comfortable) helmet. The right helmet will transform your ride from a frugal necessity to a glorious adventure atop the back of a unicorn (yes, it's that important.)
I bought my bike from bikesdirect.com for a pretty awesome price (if you don't mind doing some upgrades yourself) -- I would check out the hybrid section and see if something tickles your fancy. REI has some fantastic deals on bikes too.
Another protip - Go to a sporting goods store and stand over a few bikes to get an idea of your frame size then keep that in mind when you venture out to make your purchase.