Ideally around 1000-1500. However, would spend more if needed.
It would be a combination of both road and bike paths. I have been doing 30km with a mountain bike, but it would easier with a road bike, and plan to do longer distances with a road bike. I don't plan to race or commute with it. Luckily, I don't need to travel far to get where I need to. I'd mostly use the bike for exercising purposes.
That's a pretty decent budget, especially if you're willing to go used. You can usually get a lot more out of your money that way. Besides, with COVID, supplies at bike shops are incredibly low right now. Some things, especially parts, are back ordered into the next year. It's crazy.
My suggestion would be to look into getting a second hand cyclocross or gravel bike, rather than a straight up road bike. They will have mostly road components anyways, but will allow wider tires and more upright sitting position for better comfort. I have gravel, cyclocross, and road bikes and the road bike is what I ride the least by a long shot. In fact, I tend to only ride my road bike on the road just because that's the only place it seems the most comfortable. Last week I took my road bike out for a ~3 hour path/pavement ride and when it ended, I felt a lot more sore than when I did that same ride on my other bikes the week before.
I'm a big fan of Kona bikes. Originally a Canadian company with a lot of bang for your buck. I'd look for a second hand Jake or Jake the Snake (cyclocross) or Rove (gravel). I've never been without at least one Kona in my stable in the last 13 years.
Giant is also a good brand that gets you a lot of bang for your buck too. Specialized has some good bikes too. Cannondale is also a decent brand, but I'm not as big of a fan of their offerings as I am with the aforementioned.
What city do you live in and what is your height?