Jody,
I'm brand new to this forum, and stumbled across the site doing another type of search (for Schwinn LeTour bicycles). As mentioned above, the type of bicycle is not too important, but the ability to be at ease and look around is while in traffic. Be sure your reach on the bike is not too great, so that you can look around and behind you during the ride. Don't simply assume that because you are in the bicycle lane, that someone won't turn in front of you. (Happened to me at ~25 mph--good falling technique allowed me to come through with only scrapes.)
I'm in the "older" category at age 56, and I average about 13.5 mph on my commute. That is a pretty comfortable pace for me, but slow for my son.
I use two bicycles. My first one is a Trek 1440 which I turned into a commute bicycle with panniers and a front bag. The second is an old Schwinn LeTour 10-speed which I've just converted to do my commuting on. I'm going to use the Trek 1440 for fitness riding. It surely changed the character of the machine when I stripped off all that weight. Anyway, what I'm getting at is that I've changed the gearing of the Schwinn by changing the inner chain ring to a smaller one. It makes the hills much easier to climb, and is very inexpensive (less than $25). So there are solutions to hills even if you have a very old ten-speed bicycle.
My advise is simply to get out there, give yourself plenty of time, and get to the train station. You will enjoy the ride, the exercise, and the people you meet.