Do you have experience backpacking, or are you going with someone who does? If you are going with an experienced hiker, ask him or her what you need to bring. Make a list. REI will have just about everything you need.
A few tips: Never scrimp on boots. This is probably the single most important piece of gear for a backpacker. You can expect to drop about $200 for a good pair. And get 2 pair of good socks while you're at it. You will also need a good Gortex outer jacket, and a good fleece or similar jacket, Windstopper material perhaps. A good H2O filter is also a must have. A backpack should fit you well, and most salespeople should know how to properly fit you, but you can find a good backpack without spending loads of cash. Depending on time of year, a down jacket may be indispensable.
When packing, pack light! i.e. 2 shirts (I've done multi day hikes with one shirt), 1 pair convertable pants/shorts, 1 knit/fleece cap, headlamp, Mag light, stove, fuel and enough food.
This list is just cursory, but should get you started.
Keep in mind, "He who hikes alone has a fool for a partner."
Cheers, let us know how it goes.
