My commuting preference is a touring (not racing) road bike since you can go pretty fast, but still can carry a load. Touring bikes are designed to go long distances with lots of weight, fairly quickly. They have lots of "braze ons" to attach fenders, racks, extra water bottle cages, etc. and are very ruggedly built, so can handle a lot of weight, which is the . For an example, see the
http://surlybikes.com/bikes/long_haul_trucker, which also comes in a disc brake version. You could get something used for better value on craigslist.
I ride in rain for most of the year, but not in snow/ice. Since my long haul trucker has 37mm tires (compared to 23mm skinny on a racing bike), I can ride on many dirt/gravel trails (not single-track) without a problem. It's as fast down hills, and nearly as fast on the flats as my racing bike, but much slower uphill because of the extra weight.
For around the neighborhood and pulling kids on the trail-a-bike, I prefer a mountain/hybrid/city bike just because it's more maneuverable at low speeds and just easy. Wide/flat handlebars are better at dealing with low-speed maneuvering and kids shifting weight on the back of the bike.