You've got a "budget", and you're gonna buy "used" (smart, more bang for your buck)...... just look at Craig's list and eBay, and see what you can find. My 13 year old nephew just scored a Yamaha DT Explorer with small practice amp, headphones for $500.
Don't expect to slide into a high end V-drum or Yamaha Xtreme for cheap. I'll be taking delivery of a Yamaha kit on Tuesday (5 pads and the drum rack) .... landed ..... off eBay ..... for $173.99. Added to a Roland TD-7 module that I got for free, very affordable e-kit. Roland TD-3, 4, 5, and 6's all should fall within your budget.