A cyclo-cross style bike is an excellent choice as an all-round general purpose useful bike, for training, commuting, utility and touring as well as some off-road riding. You can even race on it. Bianchi, Jamis, Surley, Kona + others all make excellent models.
Pick one that has threaded fittings for a luggage rack and fenders. High-end competition race bikes may lack these extra features. You can swap the knobbly CX tyres for a slicker road tread.
CX bikes are a bit of a niche product but becoming more popular. If the bike shop says Huh? find another one.