Sleep System - Kifaru, Western Mountaineering, Marmot, Montbell and several others all make good sleeping bags. Try to find one that 1. Is the size you need 2. The temp range to keep you comfortable 3. Weight to carry 4. Type of insulation you want, and 5. In your price range
I prefer an air mattress, but let your comfort be your guide.
Clothing - Lots of options. Basically cotton is severely frowned upon. I am a fan on First Lite, and KUIU among others. There are a lot of good options from strictly backpacking companies too.
Food - Consensus opinion is that meals such as Mountain House, Backpackers Pantry, etc are pretty good. If it does not have 100 calories per ounce I don''t waste time with it.
Water - Your going to need it! A reputable bladder manufacturer and filter/water drops/purification system of your choice.
Cooking System - Again many options, but I think the canister stoves are probably most popular. I prefer the Pocket Rocket or MicroRocket coupled with a titanium pot.
Navigation - GPS, map and compass for me.
Optics - Generally buy the best you can afford. Even the mid level glass is pretty good nowadays.
Hygiene Kit - Sea to Summitt powder soap stuff works well, or wet wipes and a creek bath
Survival Kit - My backpacking gear....I don't carry a separate kit.
Kill Kit - I always have a knife and game bags in my pack
First Aid Kit - Duct tape (other uses too), glue, and pain pills
Bow Kit - An extra setup string, and three allen wrenches.
I would recommend a good pack as well. Kifaru, Mystery Ranch, Crooked Horn, Badlands, Eberlestock all make good packs in various price ranges