Hey caught your other thread and followed it back to this one and thought I'd post to help you out some. I've only worked on my own 10/22 but the following has been my experience modifying and shooting it over the years.
Stocks:
For a long time I used a B&C 10/22 stock and it shot fine but the barrel pad in the front seemed to make it a little inconsistent the more rounds I put downrange and overall it felt a little blocky. I ended up sanding down the front barrel pad leaving the rear pad and then torquing the take down screw to see where it got the best accuracy. It was a little more accurate and it stayed consistent for a little bit longer but during one match I had a sudden shift in POI and had to add .4 mils to everything in the middle of the stage. Me personally, I would avoid the Magpul stock if you are looking for accuracy as opposed to replicating your full size centerfire rig and just go ahead and get the Titan stock. In the long run its going to be cheaper, the Titan has more features for the money and so far it's helped my 10/22 be more consistently accurate. Yesterday I shot my 10/22 from 50 yards to 300 and back again and the whole time my accuracy and elevation data were consistent, even bouncing back and forth between ranges. I'm a believer in the Titan 10/22 stock.
Barrels:
As far as barrels go, I've only used the Green Mountain .22 barrel and I think I paid about $100 for it but it's been very accurate with ELEY and even CCI Mini-Mags. A while back I shot six 10-round groups at 45 yards with Aguila Super Extra and CCI Mini-Mags and the average accuracy for 60 rounds was .676". IMO you don't have to spend big money to get good accuracy, a lot of it is going to be in the ammunition that you pick. Keep in mind that the rifle is a semi-auto .22 so the ammunition that you use needs to cycle the bolt reliably so you might have to try a few brands to find what gives you the best accuracy and reliability. 1:16 twist is pretty much the standard and it will shoot just about anything.
Bolts:
For a long, long time I just used the standard 10/22 bolt that the rifle always had and I thought it would be just fine. I picked a Volquartsen bolt off the prize table back in the spring and dropped it into my 10/22, wow what a world of difference. Everything just feels smoother, the buffer in the back is nice too at keeping the noise down from when it was a steel pin in the back and it has a better firing pin and extractor for better reliability. I also like that the charging handle screws in to make taking everything apart just that much easier.
Triggers:
I started modifying my 10/22 before some of this stuff was out so I ended up dropping in a Power Custom sear kit into the stock 10/22 trigger pack and it worked alright, the trigger pull isn't bad but it does take some fitting to keep the safety working properly. The trigger pull isn't the best but it is about 3 pounds so not horrible and definitely better than stock. If I had to do it all over again now I'd just buy the drop in unit from Ruger, which I think is standard in the newer 10/22's. At any rate, I briefly used a Hornet Custom trigger group but ended up going back to my modified stock unit because to me the HC trigger group didn't feel as good. If you want to go big you can try one of the Volquartsen units out, I've been very impressed by their products so far.
I hope that helps get you started.