some good ideas this is a HUUUGE reply but its a bunch of stuff I like and would have liked to have known a few years ago before buying some of the wrong stuff. Welcome to BPL and good luck in your adventures
probably the best cost-weight-performance shelter is a tarp bivy setup, you can get a water resistant bivy on backpacking light for under 100, and a tarp elsewhere for around the same price, and allows you to make a pretty tight setup for bug and water resistance and can even be used in deep winter as well by digging it in a little. Mountainlaureldesigns.com is good as well as owareusa.com
even though you said you have no sewing skill, if you are primarily doing 3 season backpacking you can use alcohol stoves, which are the lightest but not as powerful as butane or white gas, and can be made out of soda cans zenstoves.com is a great resource among others. Also check out antigravitygear.com for light cheap cookware. You probably need a stove, pot and lid, windscreen, stand, pot grips, fuel container, and lid. Use platypus, nalgene, or evernew, flexible bottles if you don't have something that will work (or empty plastic bottles!) and aquamira for water treatment, it helps to duct tape the two droppers together.
sixmoondesigns.com granitegear.com golite.com gossamergear.com (also a good place for cheap sleeping pads along with this site) are some good places to start. its tough to guess how much of a backpack you need before you own all the other gear, its handy to get it last, also if you have a lighter pack you can use the foam pad as a frame and then be more comfortable on the trail. Also a pack with some foam padding can provide the padding for your feet while sleeping. Stuffsacks are handy, but don't overdo it as well, I use one for my toiletries (first aid kit, headlamp, toothbrush and toothpaste, sunscreen, sunglasses, bandana if not in a pocket etc.) and one for my sleeping bag, and one for food.
This will probably bring your costs up. A 3/4 length foam pad is usually enough for camping, but you can also get air pads, but its pretty rough having to repair it when it eventually leaks (for repairs, you can get away with duct tape, needle and thread or floss, and some super glue or seam sealer like seam grip or silnett) for low costs you can grab a synthetic sleeping bag from a company like Big Agnes or Slumberjack. Also slightly more expensive but MUCH lighter is something like jacksrbetter.com,which offers gear that is under a lb for summer sleeping, pretty awesome. You can also make bags warmer with warm clothing...
It seems like the best set up is a baselayer (I use a smartwool mid weight zip shirt, which is pricier but WELL worth it) of wool or synthetics, merino wool, capilene, (which is always on sale somewhere online) under armor etc. there are many different ones out there, most of them similar. Most ULers find their main warmth from a windshirt (Marmot Ion, patagonia houdini, montbell UL wind parka, montane windshells, too many to name them all) and a synthetic or down jacket (backpackinglight cocoon wear, patagonia micropuff, montbell thermawrap, western mountaineering flight, alot of these as well) trying to stay under a lb with those, and then a rain jacket, which can also be found for under a lb (North face triumph and DIAD, outdoor research zealot if you can find it, integral designs eVent jackets, golite virga) also you could get a poncho tarp and shave a lb+ off your gear with something like the golite poncho tarp which costs about $50 bucks and requires some skill, but its not rocket science. Add some socks, hat (I often use a patagonia R1 balaclava, something of this weight range can be multiuse and a life saver, no windstopper though, it affects your hearing) nylon pants (underlayers and also puffy pants like the ones from BPL and montbell are reallllly luxurious for an unexpected cold night out) and gloves and you are ready for an adventure. Use your sneakers or some trail runners from innovate or golite.
Also if you decide on any BPL gear they have that 40% off sale.