Nervous Newbie Toss-Up: Hybrid or Road?

I'm in my mid-twenties and have recently decided to completely switch to cycling as a means of transportation, for many of the same reasons most people do, I suppose (savings, fitness, etc).

I am going to be going to my city's annual bike swap in a couple of weeks, and am struggling to know what kind of bike to choose. I'll be using it to get around almost exclusively on paved paths and roads in the city, so according to a lot of websites, I should get a road bike. The thing is, frankly, I find bikes pretty scary at this point. Last time I rode was several years ago, and I hit a curb funny trying to go up onto a sidewalk, and my front wheel spun around, sending me flying. I swore off bikes after that. So looking at road bikes, with their skinny tires and crazy hunched-over position makes me feel pretty nervous. A mountain bike, with heftier tires and a more upright position just seems way safer to me, since I apparently suck at riding.

The main thing is, right now, I really don't want to go fast!! I'll probably be cautiously pedaling along for a while. Should I get a hybrid bike just for the greater feeling of security and comfort? Or should I suck up my fear and get a road bike, and count on eventually getting used to it?

Thanks in advance for your help! I can't believe there's a subreddit for this!

Edit: Also, how much should I expect to spend at a bike swap where mechanics have checked over the incoming used bikes? Is $200-300 reasonable? More? Less?