Choosing a barrel and stock is extremely subjective. Are you looking to save on weight? If weight isn't an issue, do you want a 20, 22 or 24-inch barrel? Tapered or bull (.920")? Stainless, black, custom color (OD Green, Blue, Red, Gradient, Color Splash, etc.)? For the stock, do you want something foldable? Are you looking for a tactical setup? Lightweight? Laminate stock? There are a LOT of questions. And even more answers to each question.
Here are my thoughts and experiences with my personal 10/22 build.
I started with a stainless .920" bull barrel in 18" from E.R. Shaw. I put it on a Revolution Yukon Laminate Stock with a Nikon 3-9x40 Rimfire scope. At 50 yards, it was a tack driver. It was also incredibly heavy and uncomfortable to use for anything other than bench rest shooting.
I have since modified that gun and added a Tactical Solutions 16.5" fluted, non-threaded barrel in matte black with a Hogue Over-Molded stock. I swapped out the Nikon for a Bushnell red dot and added a lightweight bipod to the front sling swivel (although I don't keep it on there when shooting off-hand). This is significantly lighter and much easier for me to shoot. I can shoot from a bench or off-hand and at 50 yards it too is a tack driver.
Personally, I'm not a bench-rest style shooter. I like to plink and shoot off-hand a good bit. I don't typically shoot paper targets so for me, I wanted something lightweight and fast-handling. I think my build is just that and fits my needs exactly.
From my experience, Revolution and Hogue both make great stocks. I'm sure there are other stock options out there that are equally as good, but I have no experience with them. From my experience, the E.R. Shaw barrel was excellent in accuracy, but very heavy. The Tactical Solutions is equally as accurate, but significantly lighter. I've read great things about Green Mountain, Whistle Pig and Volquartsen.
I can also recommend a trigger job and extended bolt handle as two easy upgrades that will go a long way for function.
This forum has a lot of members with a lot of great information. Stick around and you're sure to find what you need.
Welcome to the forum. Let me know if I can help out further.