This is going to irritate some people, but here goes...
Assuming that when you say offroad, you mean that it is going to be relatively minor terrain, maybe up to rain ruts and baby head sized boulders, right?
What you want is an ATB, or all terrain bike. These are generally right in your price range and have an 80mm to 100mm travel front shock and are hardtails- without rear suspension.
Your budget should see Shimano Alivio or Deore components or SRAM 5.0. Both are equally suited to your use. Forget the idea of any carbon fiber frames (whole or part) and concentrate on an aluminum or steel frame. Disc brakes at this level will be mechanical models meaning that they will be cable actuated rather than hydraulic. Avoid disc brakes unless they are either Shimano or Avid... Promax is OK but they tend to wear out pretty quickly. You'll definitely want to have linear pull, or "v" brakes and at your price there should be no problem getting Avid or Shimano. Promax v brakes aren't terrible but shouldn't be your first choice.
To lean towards the road you should try to stay with wheels that can handle 26 x 1.75 or thinner tires. Really fat tires are a drag although they do a nice job in the muck... it all depends where you are going to spend most of your time.
Regarding brands, you'll see the best value from Diamondback, KHS, Raleigh, and other "second tier" names. Trek, Cannondale, and Specialized tend to have one level lower components than other brands at the same price (but not always). Don't go by brands so much, but what fits you best.