If you plan on making it a slow-build project, it should be fine. Like you said, first thing, new trigger, retorque the action screws to 65 inch-pounds. Work from there. Typically, with good brass and good quality handloads, even the new Remingtons are going to shoot decent unless something is very wrong. Make sure to scrub that brand new unfired barrel down to the white, and make sure that bore is surgically clean before ever firing a round. Then, right before firing your first round, run a wet patch covered in RemOil down the bore. A dry bullet on a brand new squeaky-clean dry bore is going to have a good bit of friction. The RemOil will help the bullet glide better and will help evenly smooth out the rifling in your bore (break-in). I think this step is where a lot of folks screw up.
Brownings are excellent actions to build off of, but like you said, not many smith will touch them. My smith has done several of them, and said that exact same thing when I brought him my ABII to build. He said, once you get the factory barrel separated from the action, and you clean up the red loctite-like material out of the receiver threads, then from there on out, rebarreling it will be no different than a 700.