If you don't read anything else I've written here, at least do as others have said, and read all the different gear lists in peoples profiles. See what everyone is using and what kind of pack weights they are getting. Compare the weights, prices, and features of the diffent brands/models and see what suits you best.
Sorry for the long winded post to follow, but I know how much I wish I knew more when I first got into backpacking.
How much money are you looking to spend?
That will determine a lot. You can go relatively light weight without spending a whole lot, but if you want to go really lightweight, the more you spend, the lighter/more comfortable you can get.
An example of this is buying a zlite sleeping pad for $40, or a neo-air for $120. The neo air will be more comfortable and easier to pack, while the zlite will obviously be cheaper, and more versatile as a sit pad for breaks, etc. They are close to the same weight, but I believe the new version of the neo air shaved off a few ounces.
Similarly, you can get a relatively cheap synthetic sleeping bag, or spend over $300 on a super light down quilt.
Another question you should ask yourself is, "How into backpacking am I going to get?" If you'll go once or twice a year, and just do 1 or 2 nights at a time, and low mileage, it probably isn't worth spending a lot of money.
If however, this turns into something you do at least once a month, or you like to do high mileage, or you're doing longer trips, then you will probably end up upgrading your gear anyways, which means you will have spent twice the amount of money. I wish I would have just bought my dream list when I first got into backpacking, but I didn't have this wonderful forum at the time.
What do you need?
* Shelter: tarp + bivy or Tarp + bugnet(innernet) or freestanding tent. Unless you will never go when there is rain, no need for tarp. Or when there is never bugs, no need for the bivy or innernet.
******Lightest but expensive options: zpacks.com, tarptent.com, sixmoondesigns.com, mountainlauraldesigns.com
******Cheapest option: Sometimes chain sports stores have decent tents for sale, but these are generally a little heavier, but easier to set up since they have poles and are freestanding. Hell, walmart has a 5lb. tent for $60 if you want to go real cheap.
* Sleeping system: sleeping bag or sleeping quilt. synthetic or down. Temperature range? Will you wear your insulating clothing to bed? This will allow you to get a warmer rated bag/quilt. Also you'll want a sleeping pad, this will factor into how warm or cold you stay at night.
******Lightest but expensive options: katabaticgear.com, neo air sleeping pad.
******Cheapest option: Any chain sports store, zlite sleeping pad.
* Backpack: As was mentioned, buy this LAST! Get one big enough to hold all your gear, and try as many on as possible, with weight in them. The weight of your gear will determine how comfortable it is. Sure you can save 2lbs. but what does it matter if it makes your load feel like your carrying an elephant. Conversely, there is no sense in carrying a 5lb. pack if the rest of your gear/food/water only weighs 15lbs.
******Cheap, expensive, try them all on with the weight of what you will carry. Don't forget to add the weight of your water, that adds 2-6lbs. depending on how much water you carry.
* Clothes: Wear what you'll hike in, then add some insulation(i.e. jacket) for sitting around at camp. Maybe an extra pair of socks in case one gets wet. A beenie and gloves depending on the weather. I love wool, but I'll just suggest to stick with synthetics, they dry much faster, and are way cheaper. For the jacket, synthetic for cheap, or down if you want the lightest/warmest(nunatakusa.com)
* Rain gear: Dry-ducks if it is likely to rain. If not, I bring a cheap $1 rain poncho, just in case. Weighs like an ounce. You could go more expensive, but this seems to be the one area where price doesn't necessarily equate to weight savings.
* Water purification: Drops or tabs are the lightest, but I hear don't taste so good, and you have to wait a long time after you add them. Personally, I plan to buy a Sawyer squeeze filter to replace my UV sterilizer. I own a pump, but I never bother to bring it anymore.
* First aid: Doesn't need to be anything more than a few bandaids, painkillers, peptobismol, tick tweezers and some moleskin. Don't bother with anything more than that. Oh, and I'll put bug spray in this category. Just repackage it. You don't need a whole bottle for a two day trip...
* Food: Commercial dehydrated food(mountain house) will probably be the easiest way to go for dinner right now. I do two packets of instant oatmeal for breakfast, and meal bars/trail mix/jerky for lunch. Test your stove system at home before going out, so you know it works, and how much fuel to bring.
******Lightest but expensive options: Caldera Keg GVP.
******Cheapest option: Look up how to make an alcohol stove and windscreen out of beer cans.
* Food storage: Check the rules where you will hike. Some places require a bear canister. They are heavy and hard to pack, and generally suck, on the plus side they double as a chair, and you don't have to hang anything. Otherwise, learn how to hang your food. You'll need a sack for your food, and anything that smells like chapstick, lotion, etc. and a length of cord. Kelty trip teaze is relatively light and easy to get ahold of.
* Miscellaneous: Chapstick, sunglasses, brimmed hat, lighter, map/compass, purell for cleaning your hands after restroom breaks, a few squares of TP(not the whole roll), camera?. I recommend hiking sticks too. They take a lot of weight off you're knees. You won't really be able to tell, but they do, trust me, I know from painful experience. Just get some cheap ones at walmart for now. You will need them if you are not using a freestanding tent anyways. Add a few feet of ductape to your first aid kit for repairs, and that should be it!