At one time, they carried .38+P ammo loaded with 158g semi-waddcutter hollow point at ~850fps.
I believe the "standard" .357Magnum round was/is a semi-jacketed hollow point running somewhere around 1250fps. Federal Lot C357E would be a good example of such a round and one that I've emulated for my carry gun. It is stout, but not as snappy as the 125g loads approaching 1500fps.
federal has re-introduced it's Nyclad load. This is a great older load and was one of the early HP loads. It's a very soft lead HP with a nylon coating over it. It reliably opens up at .38 special velocities. I plan on gettting several boxes when I see some available.
As to the FBI load, I remeber it being a 158gr SWC-HP at yes, around 850 or so FPS. For .38 velocity loads and HP's, I'd reccomend the Hornady Swaged SWC-HP. It's a fairly soft bullet and is very accurate in all of my .38's. The soft bullet allows good expansion at velocities under 1000fps. Reminds me I need to order some more here soon!