FMJ is the way to go for a few hundred rounds. Lube the gun properly and fire away. FMJ will smooth out the bore a bit, and the power factor of FMJ allows all the internal components to "seat" themselves to each other, for additional reliability and smoothness.
I usually take it home, clean and lube it, then take it out and fire a couple hundred rounds of hardball. Either factory or reloads. I figure by 500 rounds it should be about broken in, but not always. Some take longer.
I always try to break in my guns with between 500-1000 rounds in one sitting (usually the same day I buy the gun). The one exception was the NAA Guardian. After 250 rounds I had a blister on my right index finger that ruptured. As a consequence, the gun is having its trigger contoured. I have a SIG P229 that didn't start running smooth until it had about 900 rounds af Federal 180gr through it. On the other hand, I have a USP that has never had any problems from the get-go. Ditto for my revolvers (S&W).
When I pick up a new gun (new for me anyway :lol: ), I clean & lube before my first trip to the range w/ it, shoot only FMJ & quality hollowpoints to insure reliability and shoot the first 250 rounds the 1st session and get to 1000 as quickly as I can.