Forget about a piano for that price. Just search for a decent second hand full-size MIDI keyboard, with weighted keys. They are being sold new from 400 euros and up (around 500 USD) so you might find one within your budget, second hand.
You obviously have a computer, all else you need to do is install a cracked copy of FL Studio or Cubase or any other VSTi-host, and use it to run a good piano plugin and set the audio latency to the lowest possible point.
Of course this would mean you're using cracked of software, but it's the only way I see you getting what you want for this price. At the price of slightly lower sound quality there's freeware piano plugins available. And you can also use a freeware VST host programme, just google search for them.
BTW, I forgot, you'll be needing a sustain pedal as well, as they are not included with MIDI keyboards. You only need to plug it into the designated socket on the back before hooking up the whole thing to your computer. This will drain your budget by an extra 25 quid or so, if you want to buy a pedal resembling a real piano pedal.