The PRVI Partizan is great break in ammo. Lower recoil than most other ammo and fairly cheap if you can find it online. I picked up 4 boxes from MidwayUSA last week but I am not sure if they have it in stock currently.
Most any factory, brass-cased ammo will do although some guns can be a little ammo-picky, especially during break-in. Most stick to FMJ rounds for break-in as it is cheaper and generally feeds better than some JHP. Rem UMC is widely available and usually feeds well as do most other round-nosed FMJ rounds. The Win White Box is widely available but is a flat-nosed round and may or may not feed perfectly, especially in a new gun.
I used American Eagle FMJ, it was what my LGS had when I bought my P3 and I've heard good about. My P3 shoots the AE just fine.
I think the ammo you should use is what ever FMJ you can find at this point.
Things are getting better, my LGS has some S&B and DPX in 380 the last time I was there.
Started with 200 rds of rem mc, then some GS, and then whatever, about 700 rds, all shot perfectly, and recently (blazer alum, smileys every other rd after 40 rds, maybe some spray lube would have made them work OK)????? Still have one box of Blazer alum. (only thing available in last 6 mo.) Will try to get them used up one of these days. Jim <><