I have also used the plain old 45 degree bit- making multiple passes. As has been stated, you need to make yourself a template which is used in conjunction with a bushing on the router. If you are really careful and experienced in router work you ought to be able to cut a nice barrel channel. Even with a router- depending on the template, you'll have to chisel finish the breech plug area. I personally do better with the router. I would suggest after you get the template done to practice two or three times on some scrap wood. I'm pretty certain all the "kit" gun stocks have the channel cut with a router.
NOW, as far as time, I've heard some folks can start with chisels and do the job in 20 hours. In making the template, etc, you are going to still spend some time so the decision ought to be based on what method you think is best for you. In any event, what's the big hurry, the ace in the hole for most of us is time, take plenty of time, it's often your best asset.