My take:

1. You really won't figure out what you like and don't like until you try a few different arrangements. So, don't drop a lot of money on your first bike -- you probably won't keep it very long. Buy something used that you can easily re-sell for the same price. I'd recommend keeping it under $300.

2. Keep in mind that "road," "hybrid," and "mountain" are marketing terms -- what you need to think about are A) the frame geometry that fits your body best (see point #1 ) and B) the features you want.

3. For a city commute with big hills, I'd want a bike with derailleurs (not an internally-geared hub), low gears (1:1 ratio or lower), and smooth tires. You could accomplish that in a couple of ways, but I'd say that the easiest would be to get either a hybrid or an MTB that has the gear ratios you want, and then put slick city tires on it (probably skinnier than what came with it). Tires make a huge difference; riding knobby MTB or hybrid tires on pavement is a real drag.

4. A rear rack is a must. Depending on how much stuff you need to carry and what the theft situation is like where you park, I'd recommend either panniers or (even better) Wald folding grocery baskets. The Wald baskets are heavy, but they make it easy to carry lots of stuff. You definitely don't want to be using a backpack -- bad for sweat, bad for balance.

5. Good rechargeable lights. I'm a fan of Cygolite, but others are good, too. You should be able to get a decent set for around $50.

6. You'll soon find yourself thinking about what kind of handlebars work for you. Many people find the flat MTB style, with your hands perpendicular to the direction you're traveling, pretty uncomfortable. In the city, I'd recommend upright bars that put your hands either parallel, or at a 45-degree angle to it --butterfly, moustache, albatross, North Road, and porteur are a few of the styles you might try out.