Probably what you want is a "hybrid" or "commuter" bike. Flat handlebars (like a mountain bike), smooth road tires (but a bit fatter than on a racing bike), usually the right stuff for mounting a rack and fenders.
Go down to your Local Bike Shop and look at what they have. Make sure it's a store that basically just does bicycles, not a department store that does everything. Tell them you're looking for a hybrid or commuter or "urban" bike.
It all depends on pricing in your area, but pretty much every shop has 2 or 3 hybrid bikes in the $500-$1000 price range, typically the same basic model with an upgrade option or two.
If you're worried about a steep hill, when you look at the bike, make sure that the front includes a fairly small cog and that the back includes a pretty big cog. Something where the biggest rear cog is about the same size (or even a little bigger) than the smallest front cog. That kind of thing is common on hybrids of this type. If you're looking at online specs, the front will be called a "crank" or "crankset" and have 3 numbers (you don't want one with only two front gears) such as "48/38/28" and the rear (or "cassette") will typically say something like "11-32, 8 speed" (note in this example that 28 is smaller than 32 so this does match what you're looking for). Sometimes there's marketing terms like "megarange" for this kind of thing, but the marketing terms aren't important, only having a low enough gear is.
All the major bike manufacturers make "hybrid" or "commuter" type bikes. Trek FX, Specialized Sirrus/Vita, Giant Escape, etc etc... There's differences, but the most important thing is which one fits you well and which one you like.
If $1000 is what you have to spend, consider getting a bike that's under $750 and using the other $250 for accessories like lights, fenders, a rack or basket, etc.