I'm a lifelong flatlander from back east. What impressed me most about riding in Denver when I visited two years ago, it that it's even flatter than here. The city and surrounding environs are dead flat. Now I know why fixies are so popular there. If you don't go too far west, you'll never need gears. And yet, people ride fixies up those mountains.
I took my road bike on that trip and enjoyed every mile. The roads are in very good shape, the bike path network is superb. The only time you'd need a mountain bike is off-road in the mountains. Even as a lifelong lowlander and flatlander, my road bike was perfectly adequate when we headed up the mountains on the roads. I was slower than the locals and had to stop and catch my breath every now and again, but I rode to 14,130 feet to the top of Mt. Evans with surprisingly little difficulty.
Back home, I'll never understand why missions send kids here on mountain bikes. There are no mountains for hundreds of miles, and off-road riding is illegal here except on private property. Yet every year, the Mormons send this year's crop of missionaries out into the city on shiny new mountain bikes. Even before you see the starched white shirt and black pants, you can spot a missionary by their mountain bike. And the cheesy $10 cable lock they send out with it.
In any event, there are more similarities than there are differences between new sub-$1k road bikes. Any one is as good as any other. Most have rack and fender eyelets too, something you don't generally get in more expensive models. You may also want to investigate cyclocross bikes. There are many bargain CX bikes in that price range.
As for theft, there are two kinds of locks. The first only keeps honest people honest. They are so easily defeated you might as well use dental floss. The second kind will deter most all amateur and casual thieves. None will deter a good professional. Get good locks--note the plural--and use them every time you get off the bike. This will go further to keeping your bike in your possession than will buying cheap.
Lead them not into temptation. That's the purpose of good locks--eliminating temptation.