The Moon LP3 is a fine preamp in the range, but if you want to step up your game, I don't see doing that without at least doubling your budget to $1200 or even $1500+. If you like the Moon phonostage sound – which as I recall has a very neutral presentation – maybe a Moon 310LP is a good one to set your sights on. I had one at home for a couple weeks and thought it was quite good. I considered getting it plus the outboard PSU, but ended up with a Herron phonostage (way out of your budget).
