For that kind of money, you would have to go used.

Here would be my suggestions:

Musical Fidelity A3.2 integrated
Rega Planet 2000 CD player.

Paradigm studios 100 are a good set of speakers. I can't think why anyone would tell you otherwise.

Jolida JD1501A $675
Paste the following link into your browser http://www.affordableaudio.org/JoLida1501A.pdf for some reason it won't forward you from clicking on the link.

Oppo DV-980H $170
http://www.oppodigital.com/dv980h/dv980h_review.asp

I've been using the Oppo DV-970HD for a couple of years and it works well. The DV-980H is even better.

Another possibility:

Cambridge 840A, 120w/pc

Used, audiogon. Not $1600, but 750.

http://cls.audiogon.com/cgi-bin/cls.pl?intatran&1218474829

Studio 100's like power. This amp is about 200W/pc into 4 ohms, which is the overall load that the 100's present to an amplifier. It should do fairly well. I stand corrected. Apparently the Studios have a '8 ohm rating'. Interesting. Oh well, lotsa surface area of woofers almost always equates to a need for an amplifier with power and control.

The Musical Fidelity 3.2 (as stated by Alex) is also a great amp in the right price range.