I'd advise going the other way and look for a hybrid (with a rigid fork). A drop bar tourer would also tick all the boxes.
As you're new to cycling, I reckon you'll appreciate the more upright riding position and relaxed geometry both of those will offer. You'll also get all the eyelets needed to mount a rack and mudguards for commuting, the capability to take wider tyres i.e. more "boing" on rough surfaces, and a triple chainset up front.
The latter is useful if you do plan on tackling some hills, as it will give you much lower gearing than some of the options that have been suggested. Plus, if you are very unfit, you'll really appreciate lower gears, even on the flat.
I'd also advocate second hand if you can - and save most of your budget for another day. Plus you'll also need to think about things like helmet, gloves, luggage, locks, spares and a few tools as well.