Barrels
As you probably know, a good barrel is essential for good accuracy. Without a good barrel, you won't be pleased with accuracy. There are several barrels out there ranging from Butler Creek, GM, shilen, Lilja, Clark, Clerk, and ect.
If I were you, the only two I would consider would be Lilja and GM, or Green mountain. The lilja is going to cost a lot more then the GM. However, another good alternative for a barrel that is priced in between the GM and the Lilja and is still very accurate is Clark’s barrel. Clark is one of the few barrel makers that puts an accuracy guarantee on their barrels, which I believe is 1 inch at 100 yards for their .22lr line of barrels with match ammunition.
I have a GM barrel on my 10/22 (.920 bull barrel, 20" blued), and I am VERY HAPPY with it. It is very accurate, infact, almost as accurate as some of my benchrest guns at 25 yards. Just to give you an idea, with match ammunition (Lapua superclub I have found to be very good), I can average about .15CTC groups at 25 yards.
The lilja may be a tad more accurate, so it is up to you if you want to spend up to 3 or 4 times more to get that tad bit more of accuracy, but if you are looking for the best bang for the buck, GM would be the one without a doubt.
One barrel that I honestly would NOT get is the butler creek. Although I personally have never owned one, I have heard just as many bad comments as I have good ones so I would tend to stay away from them. Having said that, I have seen a few very good shooting Butler creek barrels.
If you are looking for a lighter barrel, there are several options that you may want to consider. First of all, VQ (volquartsen) makes a very nice Carbon fiber barrel, which is much better quality and will in turn be more accurate than BC (Butler creeks) Carbon fiber barrel but it is more expensive.
There are also other barrel makers such as Whistle pig and tactical solutions, which are made of aluminum. With these barrels you do lose a bit of accuracy comparing them to a steel barrel but they can be very nice if you are going to be carrying them around or hunting with them as they are much lighter.
Another good alternative for a lighter barrel that still retains excellent accuracy is the fluted barrels. Usually you lose about 6-8oz off a barrel when it is fluted which may not sound like a whole lot, but it can be a fair bit if you are going to be shooting it offhand at all. GM (green mountain) makes several fluted barrels.
If you are going to be putting together a 10/22 and want a barrel that looks Real nice there are several options. First, you could look at the VQ snake fluted barrel, although I will say, this barrel is VERY expensive. Next up would be the Shaw barrels. They have several fluted barrels that are very nice in the looks department, and from what I hear are very accurate as well.
So basically, if money was an option, but you could still afford a barrel I would get the GM first, than the lilja, and than the Clark.
One thing to always insure when you are buying a target 10/22 barrel is that it has a bentz chamber. Basically the bentz chamber is the tightest chamber they can put on a 10/22 without having it jam. Although this is a fair bit larger of a chamber compared to some of the bolt action target guns it is still a lot tighter than the chamber that comes with a factory 10/22.
Stocks:
Again, there are many choices for stocks out there, from skinny sporter stocks, to wide benchrest stocks. On my "Ultimate" 10/22, I have a Revival industries Yukon stock in electric blue. It is made more for offhand shooting I believe (because of the very tall cheekpiece and the forend feels very good while holding it offhand), but the forend, nearer to the trigger guard has a flatter section that I rest on the bags for benchrest shooting.
The main thing to think about is what you will be using the gun for. A basic rule of thumb would be for benchrest shooting a heavier gun with a flatter forend would be the best choice where for hunting a lighter stock in synthetic would be a good choice.
There are some good choices for stocks that are made for more benchrest purposes. A good one to look at would be the Bell and Carlson anschutz style stock. It is very flat on the bottom, and has a design that will ride the bags better. Bell and Carlson make two styles of the “Anschutz style” stock.. Both of them are made from synthetic; one of them is a thumbhole and one of them is not. If you can afford it, Mcmillian makes some very nice benchrest stocks, but they are a lot of money.
You could always of course modify the factory stock, but like modifying just about anything this is going to take time... A lot of time. I modified the factory stock on mine into a more benchrest configuration while still having the forend somewhat rounded near the underside of the clip which means that it works for both offhand shooting and benchrest shooting. But generally I put this one on while I am shooting off the bench and put the other stock (Revival industries) on while I am shooting offhand.
For a cheaper approach the Hogue overmold is a nice stock.. It is well suited for hunting or in the bush because of the rubber like finish.
Triggers:
You can spend $30 to do a trigger job, or you can spend close to $300 (for a kidd).
There are several choices for triggers that I would look at. If you’re looking for a good cheap way to get a fairly light trigger (around the 2.5lbs range) the VQ hammer would be a good choice. Another choice would be Skeeters trigger kit (this is what I have on my 10/22). The trigger is around 1.8lbs, nice for all around shooting.
Again, there is also a very expensive way to do things. The Kidd trigger is a very nice trigger that will get pull weight down to around the 6-8oz range. It comes with a cost though . At around $300 US it is very pricy.
One other option would be to modify the trigger you have now. This involves changing the angle of the "hook" on the hammer, by grinding away until you are around the 3.9 Degree area I believe. Pretty hard to do if your not confident doing it. This is what I did with my 10/22, along with slight polishing, and the trigger is around the 2 pound range.