I owned the NAD PP2 and a 320BEE. The PP2 was good for the money, but not much more than that. All the phono stages you mention and others will mention will reveal that the PP2 sounds slow and closed in.
Off the one's you mention, I like the Simaudio phono stage the best. It's truly great sounding for the price new, and even better value second hand. There's nothing the PP2 does that the LP3 won't trounce. It's not even close IMO.
One that hasn't been mentioned is the Dynavector P75 (mk1 or 2). They typically show up here for well under your budget. I haven't heard every phono stage mentioned by others in this thread, but the P75 easily the best I've heard for the cash used. If my Bryston B60's internal phono stage wasn't doing the great job it's doing, the P75 is easily what I'd buy. It's very flexible in it's loading options, making it compatible with just about any cartridge on the market.
On a side note, after you upgrade the cart, you may want to look at upgrading the 320BEE. It's a great little integrated, but it's not going to show you what your vinyl chain is truly capable of. I really liked my 320BEE when I owned it, so this isn't a knock on it.