Giant and Specialized are top bike makers. Can't go wrong with either one of them. Gary Fisher, Diamondback, and Cannondale are also good. Don't get a Huffy (No! No!). You can expect to spend $350 to $450 on an entry-level bike, but it will pay for itself over time. The cheap Huffy bikes are nothing more than plumbing pipes on wheels, and you'll just be throwing your money away.
Since you're a beginner, keep this in mind: you can replace everything on the bike except the frame, so pick a frame that "fits" your body's geometry correctly. For example, did you know that there are two types of road racing bikes? (a) one for road racing and (b) one for triathlons. The tri bike's geometry is designed to work a different set of muscles than the standard road racing bike, so that the rider is able to do the run portion of the triathlon with "fresh" running muscles. Buy from a bike shop and let them do what they do best: inform, educate, and recommend.
I bought a Diamondback with a steel frame, no shocks. Steel is heavier than aluminum, but more durable and less chance of stripping a threaded screw hole (a good way to trash an expensive aluminum frame). Steel has less flex, too. You could buy titanium, the top of the line material, but that's a pricing consideration because its so expensive. I'd suggest going with a steel frame and use the money saved to upgrade the components, such as the crank, the cog, and the shifter - the parts that are most likely to break and leave you stuck in the backwoods.
Either get toeclips or shoes with clips so that you can work the pedal on the upswing - critical when going through soft sand or uphill.
Do get padded cycling shorts, preferabbly with either foam or CoolMax padding. Avoid the gel padding - the gel tends to settle in areas where there's no pressure, and that's the opposite of what you need it to do!
Don't get a kick stand - just one more thing to grab sticks and if you flip over it can become a spear.
Do get: a fat-barrel bike pump and spare tire tube, a portable bike tool kit, and padded gloves. Do get a seat pack to carry it all in. Buy a helmet to keep the branches from whacking you in the face. It might also save your life.
Suggested upgrades include front fork with shock absorbers, depending on how rugged the terrain is. Your wrists will hurt after awhile - there's more weight on them than they are used to, and factor in the impact of bouncing over tree roots and rocks and you can see where a good pair of gloves and front shocks would be welcome. I didn't get a shock-equipped bike because I didn't think I'd need that much cushion. Wrong! I don't want to spend the money to upgrade, so now I just stick to level ground - sand dunes, flat woods, such like that.
Get the quick-release bolts for your tires and seat post. Screws and nuts get lost in the woods very easily, and if you pop a tire you're going to be taking those wheels off to make the change.
Get a U-lock instead of a cable lock if you plan to ride in the city. Easier to use and less prone to getting cut.
Hope this helps.