I am in a similar position to OP -- looking at putting together a first system on a similar sort of budget, or even slightly lower. A difference is that I'm in UK. I've been reading around whilst I have been saving up and keeping my eye on ebay. An advantage of buying new kit, of course, is that it's much easier to get a demo. I'm a bit torn, though, as I know better stuff is on offer second-hand, even though it is always a bit of a gamble if you cannot audition it first. Like the OP I listen to all sorts of music and tend to like a warmer sound, so for me I'm looking for a fairly 'safe' all-rounder, which I know some people would consider a bit 'boring'. Boring is fine for me. I also want a phono stage and a decent headphone output.
I'm probably looking at getting an Arcam amp (Alpha 5+ or 6+ or 7). Most seem to agree that Arcams need efficient speakers -- I'm looking at some Missions from the same sort of era; some interesting Tannoy models pop up now and then; or possibly a new pair of Monitor Audio MR2s.
I've found this a useful guide to many of the second-hand items you encounter on ebay: http://www.hi-fiworld.co.uk/index.php/olde-worlde/295-old-buying-guide.html
Most of that stuff is British so I don't know how much you'll find in New York or what it would cost if you did. My second choice would probably be a Yamaha amp, maybe AX-396 or AX-496. Apparently these too are on the warm side so relatively bright speakers (Mission again?) should match well.
The Onkyo A-9010 has already been mentioned. If I was going to buy new, I would certainly want to get a demo of one of those. This review is well worth reading. http://www.gramophone.co.uk/feature/can-a-%C2%A3200-amp-really-be-this-good-andrew-everard-says-it-definitely-can
On turntables, I'm looking at Pro-Ject Elemental or Essential. But they're not cheap, and that stage will come later on for me.
Anyway, other people have a much better idea what they're talking about, but I thought it might be of some interest to compare notes. Good luck!