Since you are only expecting to ride 5 to 15 miles at a time and not concerned with speed, then I'd suggest a cruiser or a fat bike. Cruiser's might can be found new for not much more than your price. Fat bikes or fat tire bikes might be well outside your budget new.
These are mostly just so you'll see what I'm talking about. However if I were to ever get a bike for leisurely riding again, the Trek cruiser bikes with the swept back style handle bars will be a likely choice for me. I personally can't stand flat bars as to me they put hands in the wrong position. Since I have rolling terrain around me, I definitely want the ones that have a decent range of gearing.
https://www.trekbikes.com/us/en_US/b...=%3Arelevance#
https://www.trekbikes.com/us/en_US/b...farley/c/B336/
Buy your bike for the type of riding you expect to do now. If and when you think you want to do some other type riding, then you can get another bike for that. Nothing wrong with having more than one bike.