For a relatively cheap, jack-of-all-trades bike, I usually recommend looking for an older mountain bike, with no suspension. These work great for short-distance commuting and general transportation. You should be able to pick up one in reasonable condition for very little expense. They are rugged enough to cope with almost any riding conditions, have good brakes and gears, and can usually be equipped with a rear rack and fenders without difficulty. Swap the knobbly tyres for some slicks and you're good to go.