I've built 4 STW's in the last 3 months, plus my personal rifle that is still in the works in my shop.
1) AICS, HS Precision, Badger Ord, and CDI are good choice, all but HS use AI Mags, that being said, mags are expensive, bulky, and even the 338 Lapua length mags are a bit short for some of the Berger bullets and other VLDs which are a proven winner and popular bullet for STW. If you can find them (good luck) the older first gen AI 338 Lapua mags are long enough, but finding the bottom metal for anything but a Rem 700 footprint action isn't going to happen. Personally I don't run the detach mags on my rifles, I've had 4 of them, every one of them has hindered me in the field when trying to get a shot on an animal. The stick down too far and end up causing me to find some other shooting position. But, to each their own, and if thats something you want then thats what you want.
2) Twist rate is always a major question. I've ran 1:9 Krieger 5rs on all the builds I've done. Part of the benefit of the STW is speed, and the faster the twist rate, the slower the velocity all things being equal. If you want to base around the 140gr class bullets, 1:10 is what you need and you can get away with the 160s (168 being about the max I would recommend for it, be it not a copper solid/lead free bullet). 1:9 is more of the do all, but with Kriegers 5r and others, you get the benefit of the faster twist rate for the heavier bullet but you gain a bit of speed back you lost by going with the faster twist rate.
The last batch of Hart barrels I did were not impressive. 2 shot well, 4 did OK, not great, but not bad (3/4 MOA at 100). I try not to let a gun I built out of the shop unless it's 1/2 or better. The bigger issue was the Harts would copper foul within 4-8 shots. I don't mean a little copper foul either, I mean I push 10 inch long strings of copper out of the barrel with a patch and jag. I have good luck with Shillen Match and Douglas select match as well. Great "budget" barrel in my opinion.
3) I'm a huge fan of brakes, bigger fan of suppressors but thats a different story. Yes, some designs are LOUD, they all will increase noise but some are worse than others on noise on the driver behind the rifle. I put a Precision Armament M41 on mine ( M41 Muzzle Brake - Precision Armament
) and I've done a lot of the M11 brakes from them. Both work GREAT. I'm also a huge fan of the Holland quick discharge muzzle brakes. Not very loud, but very effective and efficient brake. Being able to watch the round impact is a big benefit for being able to quickly adjust point of aim and taking quick follow up shots. The STW isn't exactly a light recoiling round, so the more recoil management you build into it, the better you will shoot, thats a proven fact.
Any other questions, feel free to call or email us. Enjoy this awesome performing round!