You have some decisions to make.
One option is to get a bike this year, and then another one next year. So you could get a cross bike or a hybrid and
in a year or two get a road bike.
A LOT of people get back into the sport, buy a bike, and then a year or two later get another one.
A cross bike would be a good choice. Traditional road bikes used to be called the Sport category. My bike
is a Gunnar Sport, for example. That category seems to be called Plush now.
Either way, they are a lot like a cross bike. Part of the reason is that many cross bikes aren't intended for racing.
They are for guys like you, that want a bike that can do well on the street and still bomb down fire roads.
Either one would serve you well.
If it fits. Getting a good fit as an adult is crucial. You'd be surprised how many people buy a bike too small.
Talk to the guys at every shop you visit about how they find the right size for a person.
Here's an example of a sport bike.
http://surlybikes.com/bikes/pacer_complete/
One of the ways you can tell a sport bike is the brakes. They will have 57mm 'long reach' brakes.
This will let you put on larger tires for a plusher ride.
Here's the thing... either a cross bike or a sport can take a 32c tire which will do ok on a dirt road.
But the better the tire is in the dirt, the worse it will be on the road....
My standard advice is this.. go to several shops, try a bunch of bikes. Buy the bike you love.