While many believe that constructing an ultralight kit comes with high expense there is a way to blend both as long as you are open to gear not focused on high fill power or carbon fiber and other expensive upgrades.
The coolest part is that hidden amongst this vast trove of expensive high-end gear there are very dependable, while also low cost, options which are close to the ultralight requirements.
My focus on the core will be the "Big Four" as they are the bulk of your baseweight, these items are your shelter, sleeping pad, sleeping bag or backpacking quilt, and your backpack to hold them all.
These four are where I draw the line at the $500, as many times everything else will need to be adjusted based on the trip and can be expeensive or not based on what you may already own.
Big Four
When choosing your big four you have to start out with your gear that has to fit inside the backpack, so you want to choose your shelter and sleep system gear as it will help you understand the backpack size you will need, though for many ultralight gear set this will be 40L-60L depending on your size and needs.
Shelter: Gossamer Gear The One

Price: $255.00
Weight: 1.1 lbs (17.7 oz / 502 g)
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Not many options will come along at this price range and give you the weight and performance that this tent will give you while on the trail. While its the big splurge on the list it is worth all the weight it drops as the next closest "budget" tents come in around 2-3 pounds which is 1-2 pounds more than this for nearly the same cost!
A worthy mention alongside this is you could also choose the Durston Gear X-Mid 1 has won awards yearly on trail for thru-hikers and is similar to the above in price.

Sleep Insulation: HeatSeeker 20 Degree Quilt

Price: $139.00
Weight: 1.6 lbs (26 oz / 737 g)
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This is the quilt my daughter uses and they perform amazing for the cost, since you are in a tent you need to adjust the order there. Make sure to add the Ground Dweller kit to ensure the quilt has loops and straps to create attachment points for sleeping pad.
Sleeping Pad: Naturehike 5.8 R-Value Square-Standard New
Price: $81.10
Weight: 1.2 lbs (19.7 oz / 560 g)
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This is a solid performing pad for those looking at three season backpacking, when you look to move into colder weather. While there are cheaper pads they tend to perform worse and unless you want to splurge on a Nemo this will be a perfect entry point.
If you can afford a supplemental the Thinlight pad from Gossamer Gear is a perfect rest pad during the day and to put under your sleeping pad at night to help stop it shifting while dirt cheap to add into your kit, I know cause its a must carry for me.

Backpack: 3FULGEAR QiDian Hiking Backpack
Price: $53.35
Weight: 1.8 lbs (28 oz / 797 g)
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This is the first pack I started with long ago and still have after years, it is a good deal and a good first pack for a foray into ultralight backpacking, offering 40L internally and 16 within the outer pockets.
Always check out Gossamer Gear close-outs as there can be amazing packs at 50%+ off:

Now if you wanted to round this out with budget options for everything else you can pick and choose as you need to round out your pack and get ready for your longer backpacking and thruhiking adventures!
Clothing Kit
I discuss a load about creating a layering system which I would start with first if you aren't aware of how you should choose to acquire clothing. For nearly all thruhiking this kit is very lean as you will stay in the same clothing and at most end up with a second set of underwear and socks to swap out.

