Properly fit the barrel. That is where 95% of your accuracy lies, along with a mojor portion of your reliability. Since the sights are mounted on the slide, in order to achieve the best accuracy the barrel has to lock up in the same place every time. You need to insure the hood is fitted properly, the bushing is fitted properly and the feet cam on the slidestop properly. If you have that part licked, you are there.
Really, the only other thing that I can think of affecting accuracy is the crown. A new barel should be okay though.
Now, I would reccomend the Kart EZ-Fit barrel if you have never fitted a barrel before. I wish Fred would have come up with a different name. People emphasize on the EZ part and not the FIT part. This barrel has to be fitted, it just doesn't take as many tools to do it. The bushing is already properly fitted to the barrel, so you only need to fit the bushing to the slide. It is a match grade barrel by the way.
Before I forget, you should have any barrel chamber reamed also, this will insure a smooth chamber that is properly chambered for the round, and a good smith can set the freebore properly for reliability and accuracy.