Go with a top end barrel manufacturer - Krieger, Bartlein, Hawkhill, Benchmark, Brux, Rock Creek. I would avoid taking the chance on a cheaper budget barrel brand if you can afford to.
Equally important is the chambering job. The barrel blank and the gunsmith work on the barrel are the two most important factors into the accuracy and precision of a rifle. Do your homework on gunsmiths and pick wisely. There are lots of questionable gunsmiths that get promoted here unfortunately.
*Edit - since your goals are only 3/4 - 1 MOA, that should be fairly achievable with some of the cheaper options, if you do not have the budget. The budget barrels can be hit or miss, but should be able to accomplish 3/4 to 1 MOA pretty easily. You'll most likely be leaving some precision on the table, but you could luck out and get an absolute hammer. If you do have the budget, I would still recommend one of the brands I listed above - a lot better chance of getting a barrel that will out shoot you. They cost more, but that is because there is better manufacturing process and equipment, QA/QC, and experience/skillset of the workforce. No matter what the budget, I would still take it to a good, reputable gunsmith. I wouldn't save money cheaping out on a gunsmith - I know plenty of people who are kicking themselves from doing just that.
