Most older road bikes do not have low gearing and are not easy to climb up steep hills. The road bikes are generally meant for going fast (i.e. high gear range). Mountain bikes or hybrids tend to have lower gears and wider range of gears. A touring bike has some similarities to a road bike (drop handlebars, narrower tires than a mountain bike) but have the lower gearing range of mountain bikes.

Four miles isn't too far. You can start on any type of bike and decide what you need to change or upgrade after you've commuted a while. If you are buying used, try to get a decent idea of the size bike you need first. The most important thing to start is having a bike that fits reasonably well.