340 oil pump
I have a 360 that I rev to 6,500+ and can run mid 11's with a stock volume and stock pressure pump. Almost 2 seasons on it and no problems. If the engine in clean, has proper clearances, good oil, etc., you should have no problems. I use Amsoil synthetics.
I have seen tolerences on stock pumps vary. The case that comes to mind was one that had a just noticable amount of extra verticle clearance than another one. I used the tighter one.
Good advice already posted.