A hybrid, foldable or comfort bike.
A hybrid has the wider tire advantage of a mountain bike (mtb, and may have the suspension advantage too) which helps with rough city streets, but a mtb is overkill and too attractive to thieves. The narrow tires on a road bike are not really suitable for rough streets.
A foldable version of a hybrid has the advantage of being earier to transport or bring inside to prevent theft.
A comfort bike is a good basic design that works well on relatively flay city roads. It foregoes gears and may be a bit heavier ... but lends inteself to carrying loads and comfort of the rider (as the name implies).
For winter wear you need different things depending on the temperature and type of riding. Breathable rain wear over normal clothes (along with suitable boots or shoes) is sufficient for most uses, but for true exercise normal bike clothes (or polypro top) with lycra tights and a cool weather jacket is more suitable. In each case gloves and an ear muff under your helmet (you will be wearing one right?) are also needed.
See Bike Nashbar for a site with lots of clothing options. We are all different, and the requirements vary with temperature. Furthermore, clothing for a 2 mile ride to the store differs from that for a 30 mile exercise ride. You will learn as you go, but in general go for layers rather than heavy clothing since even at sub-zero you don't need that much clothing to stay warm. Hands and feet need it, and your head, but the body can be relatively lightly covered. I rode for years in Winter at temperatures down to -35F and never wore more than a couple of extra layers (although I needed a neoprene face mask and goggles, and heavy gloves and boots at that temperature).
Hope that helps.