Light=expensive with bikes, shaving those extra ounces from this or that component ain't cheap. As MegaVovaN said, a MTB or hybrid would be perfect for a mix of road and trail. If the trails are at all challenging, an MTB is the way to go. Hybrid is good for well groomed, fairly open, hard pack stuff,anything more will beat it and/or you up.
Haro makes great entry level bikes A member here who is a bike guru, used to recommend them a lot. Trek has a good entry level line up too. Plenty of bike to find out if you get the stoke or not. As mentioned above, make certain the bike fits you properly, and make a plan for maintenance and tune-ups. I suggest buying the tools and using the free guides at places like park tools, and doing it yourself. The long term cost is much lower, and if you have any mechanical aptitude, once you get over the initial learning curve, most of it is fairly straight forward.
The gear is definitely the place where the bike budget can get strained. I would start with a good brain bucket, gloves, a cheap hydration backpack, mini-pump, multi-tool, and extra tubes.
One of my great friends hangs out at bikeforums, and the gang there is definitely a great bunch. They do group buy hot deals and stuff too, so again, Mega is on the money.
EDIT: Almost forgot, ride with good tire pressure
every ride. If I had a dollar for every tube I've given away to a newb on the trails, because they got a pinch flat from riding under inflated tires, I still be in the hole cost.wise
