The last 2 new Kimbers I bought have both worked 100% out of the box.
Whatever factory FMJ you can find at a decent price is the best thing to get started. Lead might be cheaper, but a new barrel might (or might not) have some rough spots that want to grab lead. If there is any roughness, a couple hundred rounds of FMJ should smooth it out.
Your pistol probably does not need to be broken in; it just wants to be shot.