Have used every kind of bike there is for commuting, including traditional road bikes, touring bikes, cross bikes, cyclocross bikes and mountain bikes of all kinds. The good news is that all of these will work, to one extent or another. Before you pick one, though, you need to analyze your situation. How far? What kind of roads, what kind of shape? Traffic? Will you be commuting in all kinds of weather or only in nice weather? How much gear, if any, will you be packing?
I commuted several times in my life when a bicycle was my only means of transportation, as in no car, commuting right on through the winter in the snow and cold. If I had to pick one type of bike as my absolutely must get there, no matter what kind of bike, it would be the mountain bike with the right set of tires for given conditions.
The only serious disadvantage for an MTB is that it is a bit slower, so if you will be commuting 15 or 20 miles, one way, it will cost you in time. Then I would be thinking in terms of a drop bar bike with 700x35 wheels and tires. Definitely faster and actually pretty decent in lighter snow with the right tires. I used a cyclocross bike with these wheels/tires for most of my commuting, going to the MTB when the weather got nasty.
If you're new to bikes and not into road type bikes with drop bar handlebars, a cross bike with flat bars and the same 700x35 tires and wheels would do, nicely, and most of these are cheaper, too. Given their popularity, should be very easy to find one used at a great price, well within your budget.
If shopping for used bikes, though, I strongly recommend you take someone with you who really knows bikes if you are just getting back into bikes. Bikes have changed tremendously in just the last 10 years.