I suggest you look at google maps terrain feature for your area. A 500 foot climb isn't too bad, at least it not on your way into work so you can avoid being all sweaty when you arrive for work. Using google maps though, you can figure out the most direct or bike-friendly way into work (since it's downhill) and then optimize your route home to avoid the steeper sections of your return route if you wish. Obviously you don't need to take the same route there and back. For a two mile ride, almost any multi speed bike will do just fine. I suggest looking at stores like REI who have knowledgable staff and for which bikes are currently out of season (not their main focus). With multi sport stores you can often find better deals in the off season than you might find at a conventional bike shop whose sole business is bikes year round. $1000 is a very generous budget for a commuting bike. You should be able to get a good quality bike with locks and lights and all for around $700 new at a reputable bike shop. If you are willing to do a bit more digging you can score a great deal on craigslist for a used bike and save even more money. As far as the type of bike, flat-bar commuter hybrids are very popular. They are basically like a traditional road bike (lightweight and built for speed) but with features that most people find more comfortable (flat handlebars and wider tires). An example:
Scott Sub Speed 20 Bike - 2015 - REI.com
Or you could go for a typical road bike:
Scott Speedster 50 Bike - 2015 - REI.com
The Scott sub bike (or something like it) I used as an example above could be a good option. Fenders are generally important to have on a commuter if you or your employer cares about your appearance when you arrive. Even when it's dry out, fenders do a lot to keep you and your bike cleaner. The second bike I listed is also a typical style bike that is popular with commuters. In any case, I would recommend you not spend more than $700 on the bike itself and that you learn the very important nuances of how to properly lock up a bike. An expensive bike is a target for thieves and commuter bikes often must be left unattended for hours. Don't skimp on the lock, get a good u-lock. $60-90 sounds like a lot to pay for a lock but it's way better than having your bike lifted by an amateur thief. Make sure you lock it up properly every time! A good bike shop will help you choose an appropriate sized bike for yourself and equip you with helmet, lights, lock, etc as well as show you how to use everything properly.