I think MikeC is correct: the scale comes first! Here are some hints based on my experience lightening up 5-6 years ago:
Don't buy anything until you've done the following!
First get that digital postage scale.
Then set up a spreadsheet. Use the BPL gear lists as a model to organize it by system, and subtotal the weights for each system.
Weigh every individual item, no matter how small, on your scale and list it with weight on your spreadsheet. Don't trust manufacturers' weights which are usually understated. This list isn't just for weighing; eventually it will become your pre-trip checklist.
Identify the items where you could save the most weight, but don't buy anything yet.
Identify items you won't use. Do this after every trip--there are limits to this, though--don't leave the rain jacket home just because it didn't rain on your last trip!
Compare your gear list to others on BPL for ideas.
Research what's available. Mark Verber's website, http://www.verber.com/mark/outdoors/gear/index.html is a good place to start. He keeps it up-to-date and in addition to the latest high-tech he includes low budget options. Backpackgearlist.org is a good site for reviews. So, of course, is this site.
Publish your list (most spreadsheet programs will let you save as .pdf, which is what you can post here) on your profile in BPL and reference it in a post on Gear List. You will of course get a comment from MikeC about toilet paper, but that's your decision to make!
Only then start making purchase decisions. We've all made some stupid decisions on gear at some point, and you undoubtedly will, too. If you've bought used, those will be cheaper. Fortunately, you can almost always sell the items that turned out to be a horrible idea. Do try things out during the period in which you can return them. As soon as you get a shelter, set it up in the back yard, put your pad and sleeping bag inside, lie down and sit up, crawl in and out, and make sure it's what you want. Spend a couple of nights on the floor with a new sleeping pad to be sure it's comfortable for you (remember that many "established" sites are as hard as your floor!). Load up the new backpack with all your gear, adjust it and take a "hike" around the house or (if it's a clear day) around the neighborhood, making sure you keep the pack clean.
Don't be in a hurry; you can always use your old gear. Wait for sales, 20% off coupons, and such. Comparison shop at local stores and on the internet. Keep watching those used gear ads. Check thrift stores and military surplus stores.
Take your scale everywhere you gear-shop and weigh everything. Don't always get the lightest item, though; make sure it is comfortable for YOU. One of my biggest mistakes was convincing myself that the NeoAir was comfortable enough for me because I was fixated on the weight savings. That led to some very uncomfortable--and shivering--nights on the trail. Fortunately I had bought it from REI so was able to return it.
Sometimes some creative "surgery" on your existing gear will do the job--it's free!
Making your own gear is also an option. You'll find tons of suggestions in the MYOG section. To avoid having to make several iterations, first make the item out of really cheap cloth and practice sewing on scraps of the materials you'll be using before you actually tackle a complicated project.
Wait until you have most or all of your lighter gear before replacing your pack. A heavy pack is one possible candidate for creative "surgery," which can often remove a couple of pounds. You want your lighter pack to fit your new gear, not your old (it probably won't support the weight or hold the bulk of your old heavy stuff), and you want to be sure the replacement pack will support comfortably your lighter gear plus the equivalent in weight and bulk of a week's food.
IMHO, it's worth saving up for a really good and warm sleeping bag. A full-length zipper will let you ventilate or use the bag as a quilt on warm nights.
EDIT, later: Re the Gigapower canister stove: I would not call this purchase one of the poor decisions I mentioned above. Over a week, the weight of stove plus fuel comes out about equal for alcohol vs. canister stove, as demonstrated in an article on thruhiker.com (alcohol stoves use a bit more fuel). Since you're accustomed to a white gas stove, you'll feel more comfortable with the canister stove. I haven't made the switch from canister to alcohol, either! If I do, I'll use alchohol for short trips and the canister for longer trips. By the way, if you ever plan to do winter camping, hang on to that white gas stove and fuel bottles, because for well-below-freezing temperatures and melting snow for water, the white gas stove is far superior. You can use isobutane cartridges down to about 20* if you warm them up 15-20 min. under your jacket (a shivery business on a frosty morning) and use a windscreen, but otherwise the propane burns off and the butane stays liquid when it's below freezing. So while the white gas stove is too heavy for summer trips, it's great for winter!