I would buy a bike suitable for Cyclocross if you intend to participate in it in the near future. Looks like most Cyclocross bikes have fatter tyres than road bikes, so that would help off-road riding.
Trek has these Cyclocross models.
You may think it's an overkill first, but if you do want to do some serious run later, I'd suggest that you buy a bike that's meant for it. I'm saying it because I was exactly like that a couple of months ago. I was simply going to ride casually, like running errands and riding around the neighbourhood, maybe riding on the trail a bit. I bought a Trek 7.5 FX for it. I love the bike, but because I do, I ride a LOT more than I anticipated. I've racked up more than 300 miles since I bought it a month ago, including commuting to work and doing mid-range rides (20+ miles). Now I'm wondering if I should have bought a road bike instead.
The value of your life doesn't change based on the way you travel. - Dawn Schellenberg (SDOT)