Green mountain makes nice barrels. I have experience with the bull barrel and their tapered barrel and while the fluted bull barrel is a very nice looking barrel it’s too heavy for me unless you are target shooting. I prefer the tapered barrel as I squirrel hunt and this is much better suited for that. It shoots way better than me and has sent many a squirrel to acorn heaven. All pea shooter parts are hard to find at this point in history.
As others have said, carbon fiber is the way to go if you want a light weight gun. And wood is usually lighter than composite for a stock.
These barrels (above) are turned down Green Mountain barrels wrapped in carbon fiber. I prefer the Volquartsen barrels when less than $300 but finding one at the moment is gonna be tough unless you wanna boot up some extra change on eBay. Best I’ve had is proof Research carbon fiber barrels but they are expensive.
There are plain stocks modified for bull barrels up to nearly 1 inch diameter all over the place without going benchrest pro and staying lightweight, but you can also modify a birch wood factory stock pretty easy.
Do yourself a favor and go with a BX trigger! They are ready to drop in as a cassette. You can get them in the $50’s range if you look and they are very hard to beat. I’ve seen people spend $200-300 on the volquartsen parts and sweat out a trigger and shoot one of mine and get pretty pissed.
Just to throw another option into the mix, unless you are specifically looking to build I'd take a look at the Bergara BXR Carbon. I'm sure a full custom setup could perform better but I'm super happy with mine for my needs and it's a solid little performer at $599ish.
I built a target rifle a few years back using all KIDD parts. The parts are great and go together easy.
The following is the Kidd components:
20” match bull barrel bead blasted finish
Single stage trigger 2.5#
Classic Receiver in silver which also comes with the scope mount. I got it with the 20MOA version. You can get the zero or 10MOA also... or seperatly.
CNC bolt matte silver finish
Charging handle and spring assembly in silver (stainless)
Receiver pin kit
V-Block (this came with the receiver however I didn’t realized that so now I have two because I ordered it separately…..)
Take down screw (also came with receiver)
Mueller Target Dot 8-32x44 scope
Burris Zee Signature 30mm rings Medium height
The stock is a Revolution Yukon Extreme in cayenne color.