Yamaha P-155 fits the bill almost perfectly. It has speakers of a sort and can be had cheaply. Yamaha has two actions, the good one (called, GH, GH3, or GHE) and the less good one (GHS). The cheapest pianos with GH are the P-155 and CP-33. The former lacks USB-to-Host, while the latter lacks speakers. Of course, you can get a MIDI-to-USB converter and use the P-155 with VST's as well. It's just a hair less convenient. The CP-50 is newer and better, but you will not be able to get it for 1000.
I haven't liked any Casio actions I've played. I don't think they make any that are as good as GH, so I would avoid Casio if you can. If you can't afford one of the above then you are moving into semi-weighted keyboards that call themselves fully weighted, and Casio comes back to the table as an attractive option.
Other options to consider: Kawai EP3, Yamaha YDP161. Avoid the YDP141, as it uses GHS.
Good external speakers make a big difference. Studio monitors are an option, also a good Hi Fi set easily outperforms onboard speakers. I had the KRK RP8's that have been mentioned and they were ok. Not amazing. I'd recommend a studio sub and KRK RP6's instead. Better, but I think a really good hi fi set would still be better.
A good VST piano like Galaxy, Galaxy Vintage D, or Ivory will easily outperform the onboard sounds, but unless you have good speakers or headphones to listen with, you won't notice the difference much. My advice is first get a good action, then good speakers and headphones, then worry about the sounds if you are yet unsatisfied.