That's a pretty good budget - make sure you account for accessories (stuff to change a flat, floor pump, helmet, etc)
You would probably do best on a gravel bike - they're basically road bikes that can take wider tires, which will come in handy on non-paved roads. I assume you can find hybrids out there that have the same benefit and as an added plus should be rack and fender ready (Like the Trek FX line)
Many, many options out there. I'd suggest finding a good local bike shop nearby and ask them the same questions. This is also the time of year when new models roll in and old models get discounted, which can be a nice plus.