Plenty of people who post regularly on this site will love to weigh in on this, I’m sure, but here’s my 2 cents:
REI has nice commuter packages that are durable enough for some cinder trails, but not hardcore off-road biking. The reality is if you want to bomb the Frick Park trails, you’ll need a 26″ tire mountain bike. It doesn’t need to be fancy, but you’d find that your mountain bike would be a sluggish commuter, and your commuter would get wrecked on the trails. REI’s Fusion and Transfer both seem to be good all-rounders for the road and cinder paths (of which the pittsburgh parks have many). Plus, a bike like the Fusion can handle Pittsburgh’s rough road conditions year-round.
On the cheap you could convert a shock-less, older mountain bike like a Trek or Specialized to a commuter basically by putting slick 26×1.5 tires and some fenders on it. Buy yourself a front and back light, a nice rainjacket, and you should be ready lose the car.
You can also convert an old road bike (10 or 12 speed) into a decent commuter by upgrading the wheels to 700c and putting on wider, tougher tires, like 700×32 or 700×35. This option can get confusing, frustrating, and surprisingly expensive, and is probably best only if you already have a good lugged steel road bike at your disposal.
Most of the time your options are going to be framed by what you are planning to spend.